Sales c.f.(<) Median has 50% = observations on l.h.s. (35 31)5 = & above 4 70=N. We put the values to get,
|
|
- Kerrie Harris
- 5 years ago
- Views:
Transcription
1 UIT-III SOLVED EXAMPLES AVERAGES- MEASURES OF CETREL TEDECY a. Calculate the median and mode for the sales from the data given below. Sales(in Lacs): < & above o of Salesmen: Working Table: Sales c.f.(<) Median has 50% = observations on l.h.s f < ( ch ) And Md l 70 Where. f = 35; Hence class of Median is 0-5 & l=0,f=5,c=31, h= (35 31)5 We put the values to get, Md 0 =0.8 30& above 4 70= 5 Total 70 ( fm f 1) h ow, Mode= l fm f 1 f Where, fm= 5,l = 0, f1 = 16, f =10, h =5 (5 16)5 We put the values to get, Mode= 0 =.36 x b. Calculation of Median and Quartiles Q1, Q &Q3 Daily wages (Rs.):< & above o of workers: Working Table Wages(Rs) ` f c.f.(<) < & above 3 15 = Total 15 Q 1 has 5% = observations on l.h.s 4 ( ch ) And, Q l Where = f We put the values to get, (31.5 1)5 Q1 100 = Similarly, Q3 has 75%= 3 observations on l.h.s. 4 3 ( ch ) Q 4 3 l where, 3 =93.75, l=15,c=5,f=55& h=5 f 4 ( )5 Q3 15 = c. Calculate the Quartile Deviation (QD) and it s coefficient Data: Reduction in weight: o of patients Page 1 of 17
2 Calculation Table: C.I. f c.f.(<) = Total 100 Q 1 has 5% = obs on l.h.s. 4 ( ch ) And, Q 4 1 l f 100 Where = = 5, l=0, c=1,f=3,h=0 4 4 (5 1)0 We put the values to get, Q1 0 = ( IIIy, Q3 has 75%= 3 ch ) obs on l.h.s. And, Q 3 l 4 4 f Where, 3 (75 70)0 =75, l=60,c=70,f=0& h=0 Q 3 60 = Q3 Q Q ow Q.D= = 16.85& C.Q.D. = 3 Q Q3 Q d. CALCULATIO OF S.D. Ex: Compare the performance of SHIKHAR DHAWA/VIRAT KOHLI BASED O LAST 5 ODI Ans: TO COMPARE THE VARIATIOS WE OBTAI CV FOR BOTH, ODI O DHAWA KOHLI SD X VK X ODI # xM+= xM+=196 ODI # ODI # ODI # ODI # Total CLACULATIO FOR DHAWA ΣX 33 Mean= 46.6 ΣX S.D.= CLACULATIOS FOR KOHLI ΣX 64 Mean= 5.8 ΣX 4790 S.D.= Page of 17
3 S.D.= Mean x 33 X = = 5 =46.6 Mean X x 64 = = 5 =5.8 x X = 46.6 x 4790 =40.3 S.D.= X = 5.8 =46.58 n 5 n 5 C.V.= 86.5 Less C.V.=88. More Hence Dhawan was more consistent than Kohli. S.D. FOR GROUPED DATA: WHE FREQUECIES ARE GIVE, S.D. = fx X Table of calculation:- Total = fx = f DATA: Daily wages: o of workers: FOR CV WE FID MEA & SD. WHERE, fx Mean= X = 560 = 40 =14 S.D.= fx X 9680 = =6.78 And, C.V.= C.I. f X Fx f x e.g =1.5 SD.. x100 =48.44 Mean 8x1.5 = x1.5 = 150 ot 100x100 DATA CALCULATIO OF S.D. Daily wagesin100rs. o of workers: f X Mid point fx fx X=6 6x = X7= Total =40 Σfx=560 Σfx =9680 x = Page 3 of 17
4 Ex:. The data given below are the score of students in a common examination test (CET). Calculate the Standard Deviation (S.D.). Also find the coefficient of variation. Score: o of Student: Ans: Table of s.d. calculation Score f X Fx f Total = fx= x f x fx Where, Mean X = = =115.9, S.D = fx X = SD.. C.V. = x100 = x100= 44.4 Mean Ex:. Calculate the standard deviation (S.D.) from the data given below. Monthly rent paid (000Rs): o of families: C.I f x Fx fx 0 to fx Where, Mean X = = to =11.5, 10 to to 0 0 to = 840 fx fx S.D = =4.56 fx X = Page 4 of 17
5 UIT-IV PROBABILITY a. Coin problem: A group of 3 coins is tossed as a time, find the probability of getting, i. Exactly Heads ii. At most Heads Solution: When three coins are tossed up at a time the sample is S = HHH, HHT, HTH, THH,HTT,THT, TTH, TTT n(s) =8. Event A: Exactly two Head turns up. A= { HHT, THH, HTH} n(a)= 3.. na. P(A) = ( ) ns ( ) = 3 8 Event B: At most two Heads:.B: HHT, HTH, THH,HTT,THT, TTH, TTT n(b) =7... nb ( ). P(B) = ns ( ) = 7 8. b. Dice Problem: A pair of fair dice is rolled. Write down the sample space and find the probability that, the sum of dots on the uppermost face is i) 6 or 10. ii) Multiple of 4. iii) < 6. Solution: When a pair of dice is rolled, the sample space is S= (1,1), (1,), (1,3),( 1,4), (1,5), (1,6), (,1) (,6).. (5,6), (6,6) n(s)= 36. To find the probability we define the events, i) Event A: the sum of dots on the uppermost face is 6 or 10. A= {(1,5) (5,1), (,4) (4,) (3,3) (4,6) (6,4) (5,5)} n(a)= 8... na. P(A) = ( ) ns ( ) = 8 36 ii) event B: The sum of the dots on the uppermost faces is divisible by 4. B: {(1,3),(3,1),(,),(,6),(6,),(3,5),(5,3),(4,4),(6,6)} n(b)=9... nb ( ). P(B) = ns ( ) = 9 36 =0.5. iii) event C: the sum of the dots is < 6. C: { (1,1),(1,),(1,3),(1,4),(4,1)(,1),(,),(,3),(3,1),(3,)} n(c) = nc ( ). P(C)= ns ( ) = UIT-V: DECISIO THEORY a. Solve the Decision problem using MAXIMAX, MAXIMI & LAPLACE criteria Pay-off Table MAXIMAX MAXIMI MAX(AVERAGE) Stock/Demand Col A Max Col B Min Col C Average A MAX TOATL/4= 50 A A A MAX Total Page 5 of 17
6 b. Solve the Decision problem using MAXIMAX, MAXIMI & LAPLACE criteria Action/ States of nature A1 A A3 Optimal Decision S S S Max 700 MAX A Min MAX 60 A3 Average MAX A c. Solve the Decision problem using EMV criteria EMV criteria: We calculate the EMV values as follows EMV (A!) = 0x0.3 +5x0.4 +(-1)x0.3= Max EMV (A) = 8x0.3 +5x x0.3 = 5.6 EMV (A3) = -10x0.3 +5x x0.3= Hence the optimum decision is A1 Probability d. Solve the decision problem using Minimax Regret criteria Pay-off Table Regret Table Mark max for the States of nature Action/ States of A1 A A3 A1 A A3 nature Action Pay-off Table State of nature S1 S S3 A A A S = S = S = Max regret Min(Max) 810 e. Solve the Decision problem using EOL criteria Pay-off We prepare the Regret (OL) table as follows Action State of nature S1 S S3 A A A Action State of nature S1 S S3 A1 0-0 = =0 A 0-8= =5 A3 0-(-10)= EOL (A1) = 0x0.3+0x0.4+11x0.3 = Min EOL EOL (A) = 1x0.3+0x0.4+6x0.3 =5.4 EOL (A3) = 30x0.3+0x0.4+11x0.3 = 1.3 Optimal Decision: A1 Page 6 of 17
7 TUTORIAL ASSIGMET:-I Unit-II: PERMUTATIOS & COMBIATIOS Q1 Evaluate the following, i) 5 P P ii) 8 P P 4 iii) 10 P P 7 iv) 8 C C 3 v) 8 C C 7 Q. In how many possible the letters in the word FATHER be arranged so that, a) All the vowels are always together b) they are not together Q3. Five books on Mathematics, 4 books on English & 3 books on History are to be put in a shelf in a row. In how many possible ways can this be done so that, Books of same subjects are always together Only English books are together o two Mathematics are together Q4. A box contains 6 Green & 5 Red balls, a pair of balls is drawn at random. Find the no of possible selections so that, Both the balls are of same colours. They are of different colours Only red balls are drawn Q5. In how many possible ways 3 cards can be drawn from the pack of 5 cards so that, i) all 3 are Ace cards; ii) there are two kings and one queen iii) cards are of same suit TUTORIAL ASSIGMET:-II Unit-IV: PROBABILITY & RADOM VARIABLES 1. A cubic die is rolled down. What is the probability of getting, a) o of dots <4 b) no of dots as multiple of 3. A group of 3 coins is tossed up at a time. Find the probability that, a) Only 1H turns up b) there are more H than T 3. A pair of unbiased dice is rolled down. Find the probability that, a) sum of the dots is <6 b) the sum of the dots is 7 or cards are drawn from the pack of 5 cards. Find the probability that, a) all 3 are Ace cards b) all are of same suit c) there are kings & 1 queen 5. Given P(A)= 0.5, P(B) = 0.6 & P (A B) = 0.4 Find, i) P(A B) ii) P(A/B) iii) (only A) 6. For independent events A & B, P(A) = ½, P(B) = ¾. Find, i) P(A B) ii) P(only B) &iii) (only A) iv) P(Only One) 7. A problem on Maths is given to students A, B who attempt it independently. What is the probability that, i) the problem is solved? ii) it is solved by only one? Given that their chances of solving are 1/3, & 3/4 respectively. Page 7 of 17
8 TUTORIAL O:III Unit-IV:EXPECTED VALUE & VARIACE 1. Find the expected value & variance of the r.v. X defined as The no of Heads in the experiment of tossing a unbiased coin four times.. Find the Mean & Variance of the r.v. X from the following probability distribution. X p(x) Find the value of k so that the given p(x) represents a probability distribution. Hence find the expected value of X. X: p(x): k Find the Expected value and Variance of the r.v. X for the given probability distribution. Hence find the expected value of X. X: P(x): A man tosses a cubic die in a fun & fair game. According to the terms of the game. He earns, Rs10/- if the of the dots is multiple of 3, Rs15/- if the no of dots is less than 3 & earns nothing otherwise. Find his expected gain from the game if he has to pay Rs10/- as the entry fee. TUTORIAL O:IV Unit-V:DECISIO THEORY-I 1. Suppose that a decision maker faced with three decision alternatives (Acts) and three state of nature(events) with the following pay-off table: Action State of nature E1 E E3 A A A Solve the Decision problem using, a) Maximin b) Minimax regret c) Minimax Page 8 of 17
9 . Solve decision problem using Minimax regret criterion: Event E1 E E3 Action A A 8 8 A A Determine the best decision according to EMV criterion. Action/Events E1 E E3 A A A Probability: TUTORIAL O:V Unit-V:DECISIO THEORY-II 1. Draw a decision tree diagram to show the solution to the decision problem using EMV criterion: Event A1 A P(E) Action E % E 8 0% E % E %. Draw a decision tree for the decision problem below and state the best possible decision. Use EMV criteria. Product/Market Poor Average Good demand P Q P(Demand) 30% 55% 15% Page 9 of 17
10 TUTORIAL ASSIGMET:-VI Unit-III: AVERAGES (MEASURES OF CETRAL TEDECY) 1. The score of students in a class test are given below. Find the values of Mean, Median & Mode. Also count the no of students with score above the Mean score The closing price of shares on 5 trading days of the market are as follows, Calculate the mean price. Closing price(rs): o of shares: The Height of students in a class is given below. Calculate the values of Mean & Median. Height in cms: o of students: Calculate the combined mean from the data given below. Sample I II o of items: Means weight(kgs): The daily wages paid to the workers are given below. Wages in Rs: < & above O of Workers: Calculate the Median & 3 Quartiles. Hence state the wage limit that covers middle 50% of workers. TUTORIAL ASSIGMET:-VII Unit-III: DISPERSIO(MEASURES OF VARIATIO) 1. Calculate the QD &it s coefficient. Sales Range (in LacsRs.) : Below o of salesmen: The score of candidates in a CAT examination is shown below. Calculate S.D. & C.V. Score: o of Candidates: The data given below read the price range of car sales over the period of six months. Calculate the Coefficient of Variation. Price (in Lacs Rs.): o of cars sold (in 100): Calculate the combined S.D. for the data below Sample I II o of items: Mean weight (kgs): S.D. 3 4 Page 10 of 17
11 TUTORIAL O:X Unit-II:LIEAR PROGRAMMIG PROBLEM 1. Solve the following LPP by graphical method. Min Z= 150x+100y s.t. 6x+y 6; x+4y 6; x & y 0. Solve the following LPP by graphical method. Max Z= 6x+5y s.t. 4x+5y 0; x+6y 1; x& y Solve the following LPP by graphical method. Min Z= 10x+15y; s.t. 3x+y 3; x+y 3; x+y 4; x& y 0 4. Solve the following LPP by graphical method. Max Z= 16x+15y s.t. 4x+5y 0; x+6y 1; x& y 0 TUTORIAL O: VII Unit-I: SAHRES & MUTUAL FUDS 1. Calculate the 1.5% on the purchase of 300 Rs.65/-.. Calculate the dividend on 50 shares of FV 5/- 90/- 3. If a dividend of Rs. 150 is earned on 150 shares of FV /-. Find the rate of dividend earned. 4. Mr. Akash purchased 00 shares of 575/- & sold for 650/- each after receiving a dividend of 40% on FV 5/-. Calculate the % profit to him if he paid % brokerage. 5. Miss. Babita sold 00 Rs 10/- Rs.90/-.She invested the amount in buying 150 other Find the extra amount required if any, when the brokerage paid was 1.5% 6. Miss. Anju invested Rs in buying certain ten rupee Rs.90/-. He sold 1/3 rd of 15/- after 10 days and the 110/- at the end of year after receiving a dividend of 10%. Find the gain to her in the transaction. TUTORIAL O: IX Unit-I: SAHRES & MUTUAL FUDS 1. Calculate the amount of entry load on the purchase of 500 units at AV Rs /-.. Mr Akash sold 400 units of HDFC mutual fund at AV Rs. 15/- & purchased SBI mutual fund at AV Rs.78.5/-. Find the no of units purchased when load of.5% was applied in both the transactions. 3. If the AV of a MF unit is increased from 8 to 45 in one year, what is the % growth? 4. Anand invested Rs.1Lac in the gift fund of HDFC Mutual fund at AV of Rs. 8/-.He sold the units at AV Rs.3/-after receiving a 5%. Find the net % gain to him, if the load was.5% on both the transaction Page 11 of 17
12 QUESTIO BAK SEM-I SECTIO-I (MATHS) Unit-I: SHARES & MUTUAL FUDS 1. Mr. Ajay invested Rs in buying certain ten rupee Rs.90/-.He sold half of 100/- after 10 days and the 80/- at the end of year after receiving a dividend of 10%. Find the gain or loss to Mr. Ajay in the transaction.. Calculate the sale value of 500 Rs. 45/- if brokerage 0.3%.is applied. 3. Calculate the amount of brokerage paid on the purchase of 50 shares of FV Rs.10/-@ Rs.75/- when brokerage charged is 0.35%. Also calculate the purchase value. 4. Calculate the amount of 40% earned on 00 shares of F.V. Rs 5/- which were purchased at Rs.55/- each. 5. Mr. Rajesh bought 500 shares of FV Rs.150/-. He sold 40% of 180/- and the 5/- at the end of year after receiving a dividend of 5%. Find the net % gain to Mr. Rajesh in the transaction. Brokerage of 1.5 % is applied on both the transaction. 6. Mr. Shah invested Rs.43680/- in buying certain ten rupee Rs.91/-. He sold half of 100/- and the 80/- at the end of year after receiving a dividend of 10%. Find the gain or loss to Mr. Shah in the transaction. 7. The AV of a mutual fund increased from 48 to 64 within a year. Calculate the rate of growth. 8. Calculate the amount entry on the purchase of 00 units of a Mutual Fund at AV Rs.75/- 9. A person invest Rs.1,00,000 in the gift fund of HDFC Mutual fund on 11//007. Find the no of units purchased by him at AV Rs. 15/- with entry load of.5%. 10. Suppose a scheme with 1,000 units ha the following items in its balance sheet: Unit Capital Rs. 10,000; Investments at market value Rs. 5,000; Other assets Rs. 3,500; Other liabilities Rs.,000; Issue expenses not written off Rs. 500; Reserves Rs. 17,000. What would be its AV? Unit-II: PERMUTATIOS & COMBIATIOS 1. Evaluate the following, 5 P P ii) 8 P P 4 iii) 10 P P 7. In how many possible the letters in the word ATTITUDE be arranged so that, All the vowels are always together 3. All the consonants are togetherfour books on PHYSICS 3 books on CHEMISTRY & books on BIOLOGY are to be put in a shelf in a row. In how many possible ways can this be done so that, Books of same subjects are always together Only BIOLOGY books are together BIOLOGY books are at end position Page 1 of 17
13 4. Six boys & Girls are to stand in a row for a group photo. How possible ways they can have a photo so that, Girls always stand together They do not stand together They stand at the end position? 5. From the digits 1,,5,6,8 & 9 a 3 digits number is to be formed. In how many possible this can be done so that, o digit is repeated Digits are allowed to repeat Only even number without repeated is formed. 6. In how many possible ways balls can be drawn out of 15 balls? 7. Find the no of possible ways to draw a pair of cards from the pack of 5 playing cards. 8. A box contains 6 Green & 5 Red balls, a pair of balls is drawn at random. Find the no of possible selections so that, Both the balls are of same colours. They are of different colours 9. Out of 6 Batsmen, 5 Bowlers & 3 Wicketkeeper a Team of 11 players is to be formed. How many ways can this be done so as to include, 5 Batsmen, 4 Bowlers & Wicketkeeper 6 Batsmen, & at most 1 Wicketkeeper 10. In how many possible ways 3 cards can be drawn from the pack of 5 cards so that, i) all 3 are Ace cards; ii) there are two kings and one queen. iii) cards are of same suit. 11. Solve the following LPP by graphical method. i) Max Z= 6x+7y s.t. 4x+5y 0; x+6y 1; x & y 0. ii) Min Z= 10x+15y s.t. 3x+y 3; x+y 3; x & y 0 iii) Max Z= 0x+30y s.t. 3x+3y 36; 5x+y 50; x+y 3. iv) Max Z= 0x+30y s.t. 4x+6y 4; 3x+7y 1; x+y 5; x & y 0. v) Min Z= 1+0y s.t. x+y 3; x+y 3; x+y 4; x & y 0 vi) Min Z= 10x+15y s.t. 3x+y 3; x+y 3; x & y 0 Page 13 of 17
14 SECTIO-II (STATS) Unit-III: AVERAGE & DISPERSIO 1. What are the positional averages. How can they be approximated?. Write short note on Partition values. 3. Calculate the values of Mean, Median and Mode. Height in cms: o of students: The sum of deviations of the x values in a certain group of observations taken from 5 is 10 and that from 35 is Find the mean and no of observations in the group. 5. Calculate Median and Mode for the following distribution. Income in Rs.: o of Person: Calculate 3 Quartiles from and hence state the salary limits that include middle 50% of the employees. Salary(per day Rs): Below o of Employees: Calculate the Q.D. & it s coefficient from the data given below. Wages : < o of Workers: Calculate the Q.D. & it s coefficient from the data given below. Age : < & above o of Workers: The coefficient of Q.D. for a certain group of observations is 0. and the sum of lower and upper quartiles is 100. Fine the two quartiles and the Q.D. 10. Find the mean deviation and it s coefficient from mode for the data given below. Price of shares: o of shares: Calculate the standard deviation (S.D.) and C.V. from the data given below. Increase in height (in cms): o of children Calculate the coefficient of variation for the data given below. Earning per share(in 100 Rs): o of Shares: Find the coefficient of variation for the data given below. Daily wages: o of workers: Page 14 of 17
15 14. Compare the two groups on consistency level & state which group is more consistent. Group A B Mean S.D. 8 5 Also calculate the combined S.D. 15. Calculate the combined standard deviation (S.D.) from the data given below. Sample I II o of items: Means: S.D. 3 4 Unit-IV: PROBABILITY 16. Find the probability of getting a prime number when a cubic die is tossed up. 17. A box contains 0 tickets numbered 1-0. A ticket is drawn at random form the box. Find the probability that the number on the ticket is, a perfect square a multiple of A pair of unbiased dice is rolled at a time find the probability that the sum of the dots appearing on the uppermost faces is, i) 6 or 10; ii) multiple of 4; iii) 10 or more. 19. Three unbiased coins are tossed up at a time. Find the probability that, i) exactly Heads appear; ii) at most Heads appear. 0. Three cards are drawn from the pack of 5 cards. Find the probability that, i) all 3 are Ace cards; ii) there are two kings and one queen; iii) all are face cards iv) cards are of same color 1. Find the probability of getting a Face card when a card is drawn at random from a pack of 5 playing cards.. Given P (A) = /5, P (B) = 3/4 & P (A B) = ½. Find, i) P (AUB); ii) P (A/B); iii) P (B/A) Are events A & B independent? 3. Given P(A)= 0.5, P(B)= 0.7 & P(A B) = 0.4 Find, i) P (AUB); ii) P (A/B) iii) P( only A) iv) P(only one) 4. Find the expected value & variance of X from the probability distribution given below X: p(x): UIT V:-DECISIO THEORY 5. Define the terms for a Decision Problem i) Course of Action ii) State of ature iii) Pay-off Page 15 of 17
16 6. Explain the terms: Maximax criteria Laplace criteria Maximin criteria 7. What is the Regret or Opportunity loss? How is it used to find optimum decision? 8. Solve the given decision problem using, a) Maximin b) Minimax c) Laplace criteria. Course of Action States of nature(events) S1 S S3 A B C Obtain the best decision using Minimax criteria Action Events E1 E E3 A A A Solve the Decision problem using i) Minimax ii) Maximax & iii)laplace criteria EVETS COURSE OF ACTIO A1 A A3 E E E Given the pay-off matrix, solve the decision problem using, i) Laplace ii) Maximin iii) Maximax States of nature/ Action A1 A A3 S S S Given the pay-off matrix, solve the decision problem using, i) Laplace ii) Maximin iii) Maximax Action/Event E1 E E3 A A A A Page 16 of 17
17 33. Determine the best decision according to EMV criterion. States of nature Course of action A1 A A3 E E E Given, P(E1)= 0.4 P(E)= 0.5 P(E3)= Draw a decision tree for the decision problem below and state the best possible decision. Action Events E1 E E3 A A Probability: Draw decision tree for the following problem and suggest a best course of action (Use EMV) Action Choice of product States of Demand & profit Fair Good Best P Q Probability DO TRY ALL THE PROBLEMS O YOUR OW. Page 17 of 17
Decision Making. DKSharma
Decision Making DKSharma Decision making Learning Objectives: To make the students understand the concepts of Decision making Decision making environment; Decision making under certainty; Decision making
More informationAssignment 2 (Solution) Probability and Statistics
Assignment 2 (Solution) Probability and Statistics Dr. Jitesh J. Thakkar Department of Industrial and Systems Engineering Indian Institute of Technology Kharagpur Instruction Total No. of Questions: 15.
More informationDecision Making. D.K.Sharma
Decision Making D.K.Sharma 1 Decision making Learning Objectives: To make the students understand the concepts of Decision making Decision making environment; Decision making under certainty; Decision
More informationFall 2015 Math 141:505 Exam 3 Form A
Fall 205 Math 4:505 Exam 3 Form A Last Name: First Name: Exam Seat #: UIN: On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work Signature: INSTRUCTIONS Part
More informationHHH HHT HTH THH HTT THT TTH TTT
AP Statistics Name Unit 04 Probability Period Day 05 Notes Discrete & Continuous Random Variables Random Variable: Probability Distribution: Example: A probability model describes the possible outcomes
More informationMath 14 Lecture Notes Ch Mean
4. Mean, Expected Value, and Standard Deviation Mean Recall the formula from section. for find the population mean of a data set of elements µ = x 1 + x + x +!+ x = x i i=1 We can find the mean of the
More informationEcon 6900: Statistical Problems. Instructor: Yogesh Uppal
Econ 6900: Statistical Problems Instructor: Yogesh Uppal Email: yuppal@ysu.edu Lecture Slides 4 Random Variables Probability Distributions Discrete Distributions Discrete Uniform Probability Distribution
More informationDr. Abdallah Abdallah Fall Term 2014
Quantitative Analysis Dr. Abdallah Abdallah Fall Term 2014 1 Decision analysis Fundamentals of decision theory models Ch. 3 2 Decision theory Decision theory is an analytic and systemic way to tackle problems
More informationMTP_FOUNDATION_Syllabus 2012_Dec2016 SET - I. Paper 4-Fundamentals of Business Mathematics and Statistics
SET - I Paper 4-Fundamentals of Business Mathematics and Statistics Full Marks: 00 Time allowed: 3 Hours Section A (Fundamentals of Business Mathematics) I. Answer any two questions. Each question carries
More informationLesson 97 - Binomial Distributions IBHL2 - SANTOWSKI
Lesson 97 - Binomial Distributions IBHL2 - SANTOWSKI Opening Exercise: Example #: (a) Use a tree diagram to answer the following: You throwing a bent coin 3 times where P(H) = / (b) THUS, find the probability
More informationOpening Exercise: Lesson 91 - Binomial Distributions IBHL2 - SANTOWSKI
08-0- Lesson 9 - Binomial Distributions IBHL - SANTOWSKI Opening Exercise: Example #: (a) Use a tree diagram to answer the following: You throwing a bent coin times where P(H) = / (b) THUS, find the probability
More informationMATH1215: Mathematical Thinking Sec. 08 Spring Worksheet 9: Solution. x P(x)
N. Name: MATH: Mathematical Thinking Sec. 08 Spring 0 Worksheet 9: Solution Problem Compute the expected value of this probability distribution: x 3 8 0 3 P(x) 0. 0.0 0.3 0. Clearly, a value is missing
More information+ Chapter 7. Random Variables. Chapter 7: Random Variables 2/26/2015. Transforming and Combining Random Variables
+ Chapter 7: Random Variables Section 7.1 Discrete and Continuous Random Variables The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE + Chapter 7 Random Variables 7.1 7.2 7.2 Discrete
More informationConditional Probability. Expected Value.
Conditional Probability. Expected Value. CSE21 Winter 2017, Day 22 (B00), Day 14-15 (A00) March 8, 2017 http://vlsicad.ucsd.edu/courses/cse21-w17 Random Variables A random variable assigns a real number
More informationA.REPRESENTATION OF DATA
A.REPRESENTATION OF DATA (a) GRAPHS : PART I Q: Why do we need a graph paper? Ans: You need graph paper to draw: (i) Histogram (ii) Cumulative Frequency Curve (iii) Frequency Polygon (iv) Box-and-Whisker
More informationLecture 6 Probability
Faculty of Medicine Epidemiology and Biostatistics الوبائيات واإلحصاء الحيوي (31505204) Lecture 6 Probability By Hatim Jaber MD MPH JBCM PhD 3+4-7-2018 1 Presentation outline 3+4-7-2018 Time Introduction-
More informationRandom Variables. 6.1 Discrete and Continuous Random Variables. Probability Distribution. Discrete Random Variables. Chapter 6, Section 1
6.1 Discrete and Continuous Random Variables Random Variables A random variable, usually written as X, is a variable whose possible values are numerical outcomes of a random phenomenon. There are two types
More informationMeasures of Dispersion (Range, standard deviation, standard error) Introduction
Measures of Dispersion (Range, standard deviation, standard error) Introduction We have already learnt that frequency distribution table gives a rough idea of the distribution of the variables in a sample
More informationChapter 7. Random Variables
Chapter 7 Random Variables Making quantifiable meaning out of categorical data Toss three coins. What does the sample space consist of? HHH, HHT, HTH, HTT, TTT, TTH, THT, THH In statistics, we are most
More informationMTP_Foundation_Syllabus 2012_June2016_Set 1
Paper- 4: FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS Academics Department, The Institute of Cost Accountants of India (Statutory Body under an Act of Parliament) Page 1 Paper- 4: FUNDAMENTALS
More informationCHAPTER 10: Introducing Probability
CHAPTER 10: Introducing Probability The Basic Practice of Statistics 6 th Edition Moore / Notz / Fligner Lecture PowerPoint Slides Chapter 10 Concepts 2 The Idea of Probability Probability Models Probability
More informationProbability mass function; cumulative distribution function
PHP 2510 Random variables; some discrete distributions Random variables - what are they? Probability mass function; cumulative distribution function Some discrete random variable models: Bernoulli Binomial
More informationUNIT 10 DECISION MAKING PROCESS
UIT 0 DECISIO MKIG PROCESS Structure 0. Introduction Objectives 0. Decision Making Under Risk Expected Monetary Value (EMV) Criterion Expected Opportunity Loss (EOL) Criterion Expected Profit with Perfect
More information5.2 Random Variables, Probability Histograms and Probability Distributions
Chapter 5 5.2 Random Variables, Probability Histograms and Probability Distributions A random variable (r.v.) can be either continuous or discrete. It takes on the possible values of an experiment. It
More informationLecture 9. Probability Distributions. Outline. Outline
Outline Lecture 9 Probability Distributions 6-1 Introduction 6- Probability Distributions 6-3 Mean, Variance, and Expectation 6-4 The Binomial Distribution Outline 7- Properties of the Normal Distribution
More informationPanchakshari s Professional Academy CS Foundation: Statistic Practice Sheet
1. When mean is 3.57 and mode is 2.13 then the value of median is 3.09 5.01 4.01 d) 3.05 2. Frequency curve is a limiting form of Frequency polygon Histogram Both ( and ( 3. Tally marks determined Class
More informationChapter 3: Probability Distributions and Statistics
Chapter 3: Probability Distributions and Statistics Section 3.-3.3 3. Random Variables and Histograms A is a rule that assigns precisely one real number to each outcome of an experiment. We usually denote
More informationUNIVERSITY OF MUMBAI
Enclosure to Item No. 4.63 A.C. 25/05/2011 UNIVERSITY OF MUMBAI Syllabus for the F.Y.B.Com. Program : B.Com Course : Mathematical & Statistical Techniques (Credit Based Semester and Grading System with
More informationLecture 9. Probability Distributions
Lecture 9 Probability Distributions Outline 6-1 Introduction 6-2 Probability Distributions 6-3 Mean, Variance, and Expectation 6-4 The Binomial Distribution Outline 7-2 Properties of the Normal Distribution
More informationSTATISTICS STUDY NOTES UNIT I MEASURES OF CENTRAL TENDENCY DISCRETE SERIES. Direct Method. N Short-cut Method. X A f d N Step-Deviation Method
STATISTICS STUDY OTES UIT I MEASURES OF CETRAL TEDECY IDIVIDUAL SERIES ARITHMETIC MEA: Direct Method X X Short-cut Method X A d Step-Deviation Method X A d i MEDIA: th Size of term MODE: Either by inspection
More informationChapter 4. Section 4.1 Objectives. Random Variables. Random Variables. Chapter 4: Probability Distributions
Chapter 4: Probability s 4. Probability s 4. Binomial s Section 4. Objectives Distinguish between discrete random variables and continuous random variables Construct a discrete probability distribution
More informationDecision Analysis CHAPTER LEARNING OBJECTIVES CHAPTER OUTLINE. After completing this chapter, students will be able to:
CHAPTER 3 Decision Analysis LEARNING OBJECTIVES After completing this chapter, students will be able to: 1. List the steps of the decision-making process. 2. Describe the types of decision-making environments.
More information7. The random variable X is the number of cars entering the campus from 1 to 1:05 A.M. Assign probabilities according to the formula:
Operations Research Models and Methods Paul A. Jensen and Jonathan F. Bard Probability Models.S5 Exercises 1. From the daily newspaper identify five quantities that are variable in time and uncertain for
More informationEx 1) Suppose a license plate can have any three letters followed by any four digits.
AFM Notes, Unit 1 Probability Name 1-1 FPC and Permutations Date Period ------------------------------------------------------------------------------------------------------- The Fundamental Principle
More informationSTOR 155 Introductory Statistics (Chap 5) Lecture 14: Sampling Distributions for Counts and Proportions
The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL STOR 155 Introductory Statistics (Chap 5) Lecture 14: Sampling Distributions for Counts and Proportions 5/31/11 Lecture 14 1 Statistic & Its Sampling Distribution
More informationExample - Let X be the number of boys in a 4 child family. Find the probability distribution table:
Chapter8 Probability Distributions and Statistics Section 8.1 Distributions of Random Variables tthe value of the result of the probability experiment is a RANDOM VARIABLE. Example - Let X be the number
More informationChapter 6: Random Variables. Ch. 6-3: Binomial and Geometric Random Variables
Chapter : Random Variables Ch. -3: Binomial and Geometric Random Variables X 0 2 3 4 5 7 8 9 0 0 P(X) 3???????? 4 4 When the same chance process is repeated several times, we are often interested in whether
More informationChapter 3. Decision Analysis. Learning Objectives
Chapter 3 Decision Analysis To accompany Quantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna Power Point slides created by Brian Peterson Learning Objectives After completing
More informationSection 8.1 Distributions of Random Variables
Section 8.1 Distributions of Random Variables Random Variable A random variable is a rule that assigns a number to each outcome of a chance experiment. There are three types of random variables: 1. Finite
More information6 If and then. (a) 0.6 (b) 0.9 (c) 2 (d) Which of these numbers can be a value of probability distribution of a discrete random variable
1. A number between 0 and 1 that is use to measure uncertainty is called: (a) Random variable (b) Trial (c) Simple event (d) Probability 2. Probability can be expressed as: (a) Rational (b) Fraction (c)
More informationMA 1125 Lecture 14 - Expected Values. Wednesday, October 4, Objectives: Introduce expected values.
MA 5 Lecture 4 - Expected Values Wednesday, October 4, 27 Objectives: Introduce expected values.. Means, Variances, and Standard Deviations of Probability Distributions Two classes ago, we computed the
More informationProbability & Sampling The Practice of Statistics 4e Mostly Chpts 5 7
Probability & Sampling The Practice of Statistics 4e Mostly Chpts 5 7 Lew Davidson (Dr.D.) Mallard Creek High School Lewis.Davidson@cms.k12.nc.us 704-786-0470 Probability & Sampling The Practice of Statistics
More informationMath 14 Lecture Notes Ch. 4.3
4.3 The Binomial Distribution Example 1: The former Sacramento King's DeMarcus Cousins makes 77% of his free throws. If he shoots 3 times, what is the probability that he will make exactly 0, 1, 2, or
More informationSec$on 6.1: Discrete and Con.nuous Random Variables. Tuesday, November 14 th, 2017
Sec$on 6.1: Discrete and Con.nuous Random Variables Tuesday, November 14 th, 2017 Discrete and Continuous Random Variables Learning Objectives After this section, you should be able to: ü COMPUTE probabilities
More informationPart 1 In which we meet the law of averages. The Law of Averages. The Expected Value & The Standard Error. Where Are We Going?
1 The Law of Averages The Expected Value & The Standard Error Where Are We Going? Sums of random numbers The law of averages Box models for generating random numbers Sums of draws: the Expected Value Standard
More informationECON 214 Elements of Statistics for Economists 2016/2017
ECON 214 Elements of Statistics for Economists 2016/2017 Topic Probability Distributions: Binomial and Poisson Distributions Lecturer: Dr. Bernardin Senadza, Dept. of Economics bsenadza@ug.edu.gh College
More informationExample - Let X be the number of boys in a 4 child family. Find the probability distribution table:
Chapter7 Probability Distributions and Statistics Distributions of Random Variables tthe value of the result of the probability experiment is a RANDOM VARIABLE. Example - Let X be the number of boys in
More informationData that can be any numerical value are called continuous. These are usually things that are measured, such as height, length, time, speed, etc.
Chapter 8 Measures of Center Data that can be any numerical value are called continuous. These are usually things that are measured, such as height, length, time, speed, etc. Data that can only be integer
More informationStatistical Methods for NLP LT 2202
LT 2202 Lecture 3 Random variables January 26, 2012 Recap of lecture 2 Basic laws of probability: 0 P(A) 1 for every event A. P(Ω) = 1 P(A B) = P(A) + P(B) if A and B disjoint Conditional probability:
More informationMathacle. PSet Stats, Concepts In Statistics Level Number Name: Date: Distribution Distribute in anyway but normal
Distribution Distribute in anyway but normal VI. DISTRIBUTION A probability distribution is a mathematical function that provides the probabilities of occurrence of all distinct outcomes in the sample
More informationMATH 446/546 Homework 1:
MATH 446/546 Homework 1: Due September 28th, 216 Please answer the following questions. Students should type there work. 1. At time t, a company has I units of inventory in stock. Customers demand the
More informationThe binomial distribution
The binomial distribution The coin toss - three coins The coin toss - four coins The binomial probability distribution Rolling dice Using the TI nspire Graph of binomial distribution Mean & standard deviation
More informationA random variable (r. v.) is a variable whose value is a numerical outcome of a random phenomenon.
Chapter 14: random variables p394 A random variable (r. v.) is a variable whose value is a numerical outcome of a random phenomenon. Consider the experiment of tossing a coin. Define a random variable
More informationDecision Analysis. Introduction. Job Counseling
Decision Analysis Max, min, minimax, maximin, maximax, minimin All good cat names! 1 Introduction Models provide insight and understanding We make decisions Decision making is difficult because: future
More informationCHAPTER 6 Random Variables
CHAPTER 6 Random Variables 6.1 Discrete and Continuous Random Variables The Practice of Statistics, 5th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers Discrete and Continuous Random
More informationLearning Objectives = = where X i is the i t h outcome of a decision, p i is the probability of the i t h
Learning Objectives After reading Chapter 15 and working the problems for Chapter 15 in the textbook and in this Workbook, you should be able to: Distinguish between decision making under uncertainty and
More informationChapter 6: Random Variables
Chapter 6: Random Variables Section 6.1 Discrete and Continuous Random Variables The Practice of Statistics, 4 th edition For AP* STARNES, YATES, MOORE Chapter 6 Random Variables 6.1 Discrete and Continuous
More informationMATH 118 Class Notes For Chapter 5 By: Maan Omran
MATH 118 Class Notes For Chapter 5 By: Maan Omran Section 5.1 Central Tendency Mode: the number or numbers that occur most often. Median: the number at the midpoint of a ranked data. Ex1: The test scores
More informationExample. Chapter 8 Probability Distributions and Statistics Section 8.1 Distributions of Random Variables
Chapter 8 Probability Distributions and Statistics Section 8.1 Distributions of Random Variables You are dealt a hand of 5 cards. Find the probability distribution table for the number of hearts. Graph
More informationThe Binomial distribution
The Binomial distribution Examples and Definition Binomial Model (an experiment ) 1 A series of n independent trials is conducted. 2 Each trial results in a binary outcome (one is labeled success the other
More informationModel Paper Statistics Objective. Paper Code Time Allowed: 20 minutes
Model Paper Statistics Objective Intermediate Part I (11 th Class) Examination Session 2012-2013 and onward Total marks: 17 Paper Code Time Allowed: 20 minutes Note:- You have four choices for each objective
More informationSKM S J.M.PATEL COLLEGE OF COMMERCE GOREGAON (W)
SEM-II TUTORIAL ASSIGNMENT NO:I Course/Subject: MATHEMATICAL & STATISTICAL TECHNIQUES Unit-II:INTEREST& ANNUITY 1. Calculate the simple & compound interest on the sum of Rs.50000/- deposited for 4years
More informationSubject : Computer Science. Paper: Machine Learning. Module: Decision Theory and Bayesian Decision Theory. Module No: CS/ML/10.
e-pg Pathshala Subject : Computer Science Paper: Machine Learning Module: Decision Theory and Bayesian Decision Theory Module No: CS/ML/0 Quadrant I e-text Welcome to the e-pg Pathshala Lecture Series
More informationDecision Theory Using Probabilities, MV, EMV, EVPI and Other Techniques
1 Decision Theory Using Probabilities, MV, EMV, EVPI and Other Techniques Thompson Lumber is looking at marketing a new product storage sheds. Mr. Thompson has identified three decision options (alternatives)
More information(AA12) QUANTITATIVE METHODS FOR BUSINESS
All Rights Reserved ASSOCIATION OF ACCOUNTING TECHNICIANS OF SRI LANKA AA1 EXAMINATION - JULY 2016 (AA12) QUANTITATIVE METHODS FOR BUSINESS Instructions to candidates (Please Read Carefully): (1) Time
More informationChapter 4 Discrete Random variables
Chapter 4 Discrete Random variables A is a variable that assumes numerical values associated with the random outcomes of an experiment, where only one numerical value is assigned to each sample point.
More informationMean, Variance, and Expectation. Mean
3 Mean, Variance, and Expectation The mean, variance, and standard deviation for a probability distribution are computed differently from the mean, variance, and standard deviation for samples. This section
More informationMANAGEMENT PRINCIPLES AND STATISTICS (252 BE)
MANAGEMENT PRINCIPLES AND STATISTICS (252 BE) Normal and Binomial Distribution Applied to Construction Management Sampling and Confidence Intervals Sr Tan Liat Choon Email: tanliatchoon@gmail.com Mobile:
More informationIntroduction LEARNING OBJECTIVES. The Six Steps in Decision Making. Thompson Lumber Company. Thompson Lumber Company
Valua%on and pricing (November 5, 2013) Lecture 4 Decision making (part 1) Olivier J. de Jong, LL.M., MM., MBA, CFD, CFFA, AA www.olivierdejong.com LEARNING OBJECTIVES 1. List the steps of the decision-making
More informationTotal number of balls played
Class IX - NCERT Maths Exercise (15.1) Question 1: In a cricket math, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary. Solution 1: Number
More information6.1 Discrete and Continuous Random Variables. 6.1A Discrete random Variables, Mean (Expected Value) of a Discrete Random Variable
6.1 Discrete and Continuous Random Variables 6.1A Discrete random Variables, Mean (Expected Value) of a Discrete Random Variable Random variable Takes numerical values that describe the outcomes of some
More informationBasic Procedure for Histograms
Basic Procedure for Histograms 1. Compute the range of observations (min. & max. value) 2. Choose an initial # of classes (most likely based on the range of values, try and find a number of classes that
More information6.1 Binomial Theorem
Unit 6 Probability AFM Valentine 6.1 Binomial Theorem Objective: I will be able to read and evaluate binomial coefficients. I will be able to expand binomials using binomial theorem. Vocabulary Binomial
More information5.1 Personal Probability
5. Probability Value Page 1 5.1 Personal Probability Although we think probability is something that is confined to math class, in the form of personal probability it is something we use to make decisions
More informationFINAL REVIEW 14! (14 2)!2!
Discrete Mathematics FINAL REVIEW Name Per. Evaluate and simplify the following completely, Show all your work. 1. 5! 2. 7! 42 3. 9!4! 3!10! 4. 24!19! 22!21! 5. 4! (7 5)! 6. 46! 45!23 7. 9 5!3! 18 2!4!
More informationFINAL REVIEW W/ANSWERS
FINAL REVIEW W/ANSWERS ( 03/15/08 - Sharon Coates) Concepts to review before answering the questions: A population consists of the entire group of people or objects of interest to an investigator, while
More information19 Decision Making. Expected Monetary Value Expected Opportunity Loss Return-to-Risk Ratio Decision Making with Sample Information
19 Decision Making USING STATISTICS @ The Reliable Fund 19.1 Payoff Tables and Decision Trees 19.2 Criteria for Decision Making Maximax Payoff Maximin Payoff Expected Monetary Value Expected Opportunity
More informationEDO UNIVERSITY, IYAMHO EDO STATE, NIGERIA
EDO UNIVERSITY, IYAMHO EDO STATE, NIGERIA MTH 122 :ELEMENTARY STATISTICS INTRODUCTION OF LECTURER Alhassan Charity Jumai is Lecturer of Mathematics at the Faculty of Physical Sciences, Edo University Iyamho,
More informationI can use simulation to model chance behavior. I can describe a probability model for a chance process. I can use basic probability rules, including
1 AP Statistics Unit 3 Concepts (Chapter 5, 6, 7) Baseline Topics: (must show mastery in order to receive a 3 or above I can distinguish between a parameter and a statistic. I can use a probability distribution
More informationExercise 15.1 Question 1: In a cricket math, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary. Number of times the batswoman hits a boundary
More informationModule 15 July 28, 2014
Module 15 July 28, 2014 General Approach to Decision Making Many Uses: Capacity Planning Product/Service Design Equipment Selection Location Planning Others Typically Used for Decisions Characterized by
More informationElementary Statistics Blue Book. The Normal Curve
Elementary Statistics Blue Book How to work smarter not harder The Normal Curve 68.2% 95.4% 99.7 % -4-3 -2-1 0 1 2 3 4 Z Scores John G. Blom May 2011 01 02 TI 30XA Key Strokes 03 07 TI 83/84 Key Strokes
More informationChapter 8 Homework Solutions Compiled by Joe Kahlig
homewk problems, B-copyright Joe Kahlig Chapter Solutions, Page Chapter omewk Solutions Compiled by Joe Kahlig 0. 0. 0. 0.. You are counting the number of games and there are a limited number of games
More informationPart V - Chance Variability
Part V - Chance Variability Dr. Joseph Brennan Math 148, BU Dr. Joseph Brennan (Math 148, BU) Part V - Chance Variability 1 / 78 Law of Averages In Chapter 13 we discussed the Kerrich coin-tossing experiment.
More informationVIDEO 1. A random variable is a quantity whose value depends on chance, for example, the outcome when a die is rolled.
Part 1: Probability Distributions VIDEO 1 Name: 11-10 Probability and Binomial Distributions A random variable is a quantity whose value depends on chance, for example, the outcome when a die is rolled.
More informationCounting Basics. Venn diagrams
Counting Basics Sets Ways of specifying sets Union and intersection Universal set and complements Empty set and disjoint sets Venn diagrams Counting Inclusion-exclusion Multiplication principle Addition
More informationProbability Distributions for Discrete RV
Probability Distributions for Discrete RV Probability Distributions for Discrete RV Definition The probability distribution or probability mass function (pmf) of a discrete rv is defined for every number
More informationName: Show all your work! Mathematical Concepts Joysheet 1 MAT 117, Spring 2013 D. Ivanšić
Mathematical Concepts Joysheet 1 Use your calculator to compute each expression to 6 significant digits accuracy or six decimal places, whichever is more accurate. Write down the sequence of keys you entered
More informationMath 235 Final Exam Practice test. Name
Math 235 Final Exam Practice test Name Use the Gauss-Jordan method to solve the system of equations. 1) x + y + z = -1 x - y + 3z = -7 4x + y + z = -7 A) (-1, -2, 2) B) (-2, 2, -1) C)(-1, 2, -2) D) No
More information(c) The probability that a randomly selected driver having a California drivers license
Statistics Test 2 Name: KEY 1 Classify each statement as an example of classical probability, empirical probability, or subjective probability (a An executive for the Krusty-O cereal factory makes an educated
More informationRandom Variables and Applications OPRE 6301
Random Variables and Applications OPRE 6301 Random Variables... As noted earlier, variability is omnipresent in the business world. To model variability probabilistically, we need the concept of a random
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Math 131-03 Practice Questions for Exam# 2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 1) What is the effective rate that corresponds to a nominal
More informationECO220Y Introduction to Probability Readings: Chapter 6 (skip section 6.9) and Chapter 9 (section )
ECO220Y Introduction to Probability Readings: Chapter 6 (skip section 6.9) and Chapter 9 (section 9.1-9.3) Fall 2011 Lecture 6 Part 2 (Fall 2011) Introduction to Probability Lecture 6 Part 2 1 / 44 From
More informationLecture Data Science
Web Science & Technologies University of Koblenz Landau, Germany Lecture Data Science Statistics Foundations JProf. Dr. Claudia Wagner Learning Goals How to describe sample data? What is mode/median/mean?
More informationSection I 22 marks Attempt Questions 1-22 Allow about 30 minutes for this section. Use the multiple choice answer sheet provided.
Section I 22 marks Attempt Questions 1-22 Allow about 30 minutes for this section. Use the multiple choice answer sheet provided. 1) The solution to the equation 2x + 3 = 9 is: (A) 39 (B) 0 (C) 36 (D)
More informationPROBABILITY AND STATISTICS, A16, TEST 1
PROBABILITY AND STATISTICS, A16, TEST 1 Name: Student number (1) (1.5 marks) i) Let A and B be mutually exclusive events with p(a) = 0.7 and p(b) = 0.2. Determine p(a B ) and also p(a B). ii) Let C and
More informationUnit 04 Review. Probability Rules
Unit 04 Review Probability Rules A sample space contains all the possible outcomes observed in a trial of an experiment, a survey, or some random phenomenon. The sum of the probabilities for all possible
More informationTheir opponent will play intelligently and wishes to maximize their own payoff.
Two Person Games (Strictly Determined Games) We have already considered how probability and expected value can be used as decision making tools for choosing a strategy. We include two examples below for
More informationMathematical Concepts Joysheet 1 MAT 117, Spring 2011 D. Ivanšić. Name: Show all your work!
Mathematical Concepts Joysheet 1 Use your calculator to compute each expression to 6 significant digits accuracy. Write down thesequence of keys youentered inorder to compute each expression. Donot roundnumbers
More informationST. DAVID S MARIST INANDA
ST. DAVID S MARIST INANDA MATHEMATICS NOVEMBER EXAMINATION GRADE 11 PAPER 1 8 th NOVEMBER 2016 EXAMINER: MRS S RICHARD MARKS: 125 MODERATOR: MRS C KENNEDY TIME: 2 1 Hours 2 NAME: PLEASE PUT A CROSS NEXT
More information