|
|
|
- Francine Thomas
- 5 years ago
- Views:
Transcription
1 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. Number of times the batswoman hits a boundary = 6 Total number of balls played = 30 Number of times that the batswoman does not hit a boundary = 30 6 = 24 Question 2: 1500 families with 2 children were selected randomly, and the following data were recorded: Number of girls in a family Number of families Compute the probability of a family, chosen at random, having (i) 2 girls (ii) 1 girl (iii) No girl Also check whether the sum of these probabilities is 1. Total number of families = = 1500 (i) Number of families having 2 girls = 475 (ii) Number of families having 1 girl = 814
2 (iii) Number of families having no girl = 211 Therefore, the sum of all these probabilities is 1. Question 3: In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained: Find the probability that a student of the class was born in August.
3 Number of students born in the month of August = 6 Total number of students = 40 Question 4: Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes: Outcome 3 heads 2 heads 1 head No head Frequency If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up. Number of times 2 heads come up = 72 Total number of times the coins were tossed = 200 Question 5: An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below: Monthly income (in Rs) Vehicles per family Above 2
4 Less than or more Suppose a family is chosen, find the probability that the family chosen is (i) earning Rs per month and owning exactly 2 vehicles. (ii) earning Rs or more per month and owning exactly 1 vehicle. (iii) earning less than Rs 7000 per month and does not own any vehicle. (iv) earning Rs per month and owning more than 2 vehicles. (v) owning not more than 1 vehicle. Number of total families surveyed = = 2400 (i) Number of families earning Rs per month and owning exactly 2 vehicles = 29 (ii) Number of families earning Rs or more per month and owning exactly 1 vehicle = 579 (iii) Number of families earning less than Rs 7000 per month and does not own any vehicle = 10
5 (iv) Number of families earning Rs per month and owning more than 2 vehicles = 25 (v) Number of families owning not more than 1 vehicle = = 2062 Question 6: A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows: 0 20, , Then she formed the following table: Marks Number of student above 8 Total 90 (i) Find the probability that a student obtained less than 20 % in the mathematics test. (ii) Find the probability that a student obtained marks 60 or above. Totalnumber of students = 90
6 (i) Number of students getting less than 20 % marks in the test = 7 (ii) Number of students obtaining marks 60 or above = = 23 Question 7: To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table. Opinion Number of students like 135 dislike 65 Find the probability that a student chosen at random (i) likes statistics, (ii) does not like it Total number of students = = 200 (i) Number of students liking statistics = 135 (ii) Number of students who do not like statistics = 65 Question 8: The distance (in km) of 40 engineers from their residence to their place of work were found as follows
7 What is the empirical probability that an engineer lives: (i) less than 7 km from her place of work? (ii) more than or equal to 7 km from her place of work? (iii) within km from her place of work? (i) Total number of engineers = 40 Number of engineers living less than 7 km from their place of work = 9 Hence, required probability that an engineer lives less than 7 km from her place of work, (ii) Number of engineers living more than or equal to 7 km from their place of work = 40 9 = 31 Hence, required probability that an engineer lives more than or equal to 7 km from her place of work, (iii) Number of engineers living within km from her place of work = 0 Hence, required probability that an engineer lives within km from her place of work, P = 0 Question 11: Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg):
8 Find the probability that any of these bags chosen at random contains more than 5 kg of flour. Number of total bags = 11 Number of bags containing more than 5 kg of flour = 7 Question 12: Concentration of SO 2 (in ppm) Number of days (frequency ) Total 30 The above frequency distribution table represents the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval on any of these days. Number days for which the concentration of sulphur dioxide was in the interval of = 2 Total number of days = 30
9 Question 13: Blood group Number of students A 9 B 6 AB 3 O 12 Total 30 The above frequency distribution table represents the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB. Number of students having blood group AB = 3 Total number of students = 30
Total 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
Probability Exercise -1
1 Probability Exercise -1 Question 1 In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find The probability that she did not hit a boundary. Let P is the event of hitting
MATH 264 Problem Homework I
MATH Problem Homework I Due to December 9, 00@:0 PROBLEMS & SOLUTIONS. A student answers a multiple-choice examination question that offers four possible answers. Suppose that the probability that the
Math 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
d) Find the standard deviation of the random variable X.
Q 1: The number of students using Math lab per day is found in the distribution below. x 6 8 10 12 14 P(x) 0.15 0.3 0.35 0.1 0.1 a) Find the mean for this probability distribution. b) Find the variance
1. (9; 3ea) The table lists the survey results of 100 non-senior students. Math major Art major Biology major
Math 54 Test #2(Chapter 4, 5, 6, 7) Name: Show all necessary work for full credit. You may use graphing calculators for your calculation, but you must show all detail and use the proper notations. Total
MATH1215: 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
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
MATH 1324 Review for Test 4 November 2016 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Prepare a probability distribution for the experiment. Let x
Cover Page Homework #8
MODESTO JUNIOR COLLEGE Department of Mathematics MATH 134 Fall 2011 Problem 11.6 Cover Page Homework #8 (a) What does the population distribution describe? (b) What does the sampling distribution of x
Chapter 3. Discrete Probability Distributions
Chapter 3 Discrete Probability Distributions 1 Chapter 3 Overview Introduction 3-1 The Binomial Distribution 3-2 Other Types of Distributions 2 Chapter 3 Objectives Find the exact probability for X successes
VIDEO 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.
I. Standard Error II. Standard Error III. Standard Error 2.54
1) Original Population: Match the standard error (I, II, or III) with the correct sampling distribution (A, B, or C) and the correct sample size (1, 5, or 10) I. Standard Error 1.03 II. Standard Error
ECON 214 Elements of Statistics for Economists 2016/2017
ECON 214 Elements of Statistics for Economists 2016/2017 Topic The Normal Distribution Lecturer: Dr. Bernardin Senadza, Dept. of Economics bsenadza@ug.edu.gh College of Education School of Continuing and
Lecture 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
Lecture 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
Probability Distributions
4.1 Probability Distributions Random Variables A random variable x represents a numerical value associated with each outcome of a probability distribution. A random variable is discrete if it has a finite
A.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
STATISTICS 4040/23 Paper 2 October/November 2014
Cambridge International Examinations Cambridge Ordinary Level *9099999814* STATISTICS 4040/23 Paper 2 October/November 2014 Candidates answer on the question paper. Additional Materials: Pair of compasses
ST. 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
SHORT 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
Event p351 An event is an outcome or a set of outcomes of a random phenomenon. That is, an event is a subset of the sample space.
Chapter 12: From randomness to probability 350 Terminology Sample space p351 The sample space of a random phenomenon is the set of all possible outcomes. Example Toss a coin. Sample space: S = {H, T} Example:
Example 1: Identify the following random variables as discrete or continuous: a) Weight of a package. b) Number of students in a first-grade classroom
Section 5-1 Probability Distributions I. Random Variables A variable x is a if the value that it assumes, corresponding to the of an experiment, is a or event. A random variable is if it potentially can
Chapter 6 Probability
Chapter 6 Probability Learning Objectives 1. Simulate simple experiments and compute empirical probabilities. 2. Compute both theoretical and empirical probabilities. 3. Apply the rules of probability
Math 361. Day 8 Binomial Random Variables pages 27 and 28 Inv Do you have ESP? Inv. 1.3 Tim or Bob?
Math 361 Day 8 Binomial Random Variables pages 27 and 28 Inv. 1.2 - Do you have ESP? Inv. 1.3 Tim or Bob? Inv. 1.1: Friend or Foe Review Is a particular study result consistent with the null model? Learning
Random variables. Discrete random variables. Continuous random variables.
Random variables Discrete random variables. Continuous random variables. Discrete random variables. Denote a discrete random variable with X: It is a variable that takes values with some probability. Examples:
OCR Statistics 1. Discrete random variables. Section 2: The binomial and geometric distributions. When to use the binomial distribution
Discrete random variables Section 2: The binomial and geometric distributions Notes and Examples These notes contain subsections on: When to use the binomial distribution Binomial coefficients Worked examples
Comparing Quantities
COMPARING QUANTITIES 7 Comparing Quantities CHAPTER 8 8. Recalling Ratios and Percentages We know, ratio means comparing two quantities. A basket has two types of fruits, say, 0 apples and 5 oranges. Then,
MTP_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
Edexcel Statistics 1 Normal Distribution Edited by: K V Kumaran
Edexcel Statistics 1 Normal Distribution Edited by: K V Kumaran kumarmaths.weebly.com 1 kumarmaths.weebly.com 2 kumarmaths.weebly.com 3 kumarmaths.weebly.com 4 kumarmaths.weebly.com 5 kumarmaths.weebly.com
Assignment 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.
Probability Distributions. Definitions Discrete vs. Continuous Mean and Standard Deviation TI 83/84 Calculator Binomial Distribution
Probability Distributions Definitions Discrete vs. Continuous Mean and Standard Deviation TI 83/84 Calculator Binomial Distribution Definitions Random Variable: a variable that has a single numerical value
MATH CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #2 - SUMMER DR. DAVID BRIDGE
MATH 2053 - CALCULUS & STATISTICS/BUSN - PRACTICE EXAM #2 - SUMMER 2007 - DR. DAVID BRIDGE MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the
guessing Bluman, Chapter 5 2
Bluman, Chapter 5 1 guessing Suppose there is multiple choice quiz on a subject you don t know anything about. 15 th Century Russian Literature; Nuclear physics etc. You have to guess on every question.
PROBABILITY DISTRIBUTIONS
CHAPTER 3 PROBABILITY DISTRIBUTIONS Page Contents 3.1 Introduction to Probability Distributions 51 3.2 The Normal Distribution 56 3.3 The Binomial Distribution 60 3.4 The Poisson Distribution 64 Exercise
Chapter 6. The Normal Probability Distributions
Chapter 6 The Normal Probability Distributions 1 Chapter 6 Overview Introduction 6-1 Normal Probability Distributions 6-2 The Standard Normal Distribution 6-3 Applications of the Normal Distribution 6-5
Chapter 9 & 10. Multiple Choice.
Chapter 9 & 10 Review Name Multiple Choice. 1. An agricultural researcher plants 25 plots with a new variety of corn. The average yield for these plots is X = 150 bushels per acre. Assume that the yield
Edexcel past paper questions
Edexcel past paper questions Statistics 1 Chapters 2-4 (Continuous) S1 Chapters 2-4 Page 1 S1 Chapters 2-4 Page 2 S1 Chapters 2-4 Page 3 S1 Chapters 2-4 Page 4 Histograms When you are asked to draw a histogram
Chapter 4 Probability Distributions
Slide 1 Chapter 4 Probability Distributions Slide 2 4-1 Overview 4-2 Random Variables 4-3 Binomial Probability Distributions 4-4 Mean, Variance, and Standard Deviation for the Binomial Distribution 4-5
Example - 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
Lecture 7 Random Variables
Lecture 7 Random Variables Definition: A random variable is a variable whose value is a numerical outcome of a random phenomenon, so its values are determined by chance. We shall use letters such as X
Distribution of the Sample Mean
Distribution of the Sample Mean MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2018 Experiment (1 of 3) Suppose we have the following population : 4 8 1 2 3 4 9 1
STOR 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
Problem A Grade x P(x) To get "C" 1 or 2 must be 1 0.05469 B A 2 0.16410 3 0.27340 4 0.27340 5 0.16410 6 0.05470 7 0.00780 0.2188 0.5468 0.2266 Problem B Grade x P(x) To get "C" 1 or 2 must 1 0.31150 be
STATISTICS KEY POINTS
STATISTICS KEY POINTS The three measures of central tendency are : i. Mean ii. Median iii. Mode Mean Of grouped frequency distribution can be calculated by the following methods. (i) (ii) (iii) Direct
Overview. Definitions. Definitions. Graphs. Chapter 5 Probability Distributions. probability distributions
Chapter 5 Probability Distributions 5-1 Overview 5-2 Random Variables 5-3 Binomial Probability Distributions 5-4 Mean, Variance, and Standard Deviation for the Binomial Distribution 5-5 The Poisson Distribution
Unit 4 Bernoulli and Binomial Distributions Week #6 - Practice Problems. SOLUTIONS Revised (enhanced for q4)
PubHlth 540 Introductory Biostatistics Page 1 of 6 Unit 4 Bernoulli and Binomial Distributions Week #6 - Practice Problems SOLUTIONS Revised (enhanced for q4) 10-29-2008 1. This exercise gives you practice
Chapter 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
Discrete Probability Distributions
Discrete Probability Distributions Chapter 6 Learning Objectives Define terms random variable and probability distribution. Distinguish between discrete and continuous probability distributions. Calculate
Lecture 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-
Panchakshari 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
Mathematical 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
Applied Mathematics 12 Extra Practice Exercises Chapter 3
H E LP Applied Mathematics Extra Practice Exercises Chapter Tutorial., page 98. A bag contains 5 red balls, blue balls, and green balls. For each of the experiments described below, complete the given
Lecture 3. Sampling distributions. Counts, Proportions, and sample mean.
Lecture 3 Sampling distributions. Counts, Proportions, and sample mean. Statistical Inference: Uses data and summary statistics (mean, variances, proportions, slopes) to draw conclusions about a population
Overview. Definitions. Definitions. Graphs. Chapter 4 Probability Distributions. probability distributions
Chapter 4 Probability Distributions 4-1 Overview 4-2 Random Variables 4-3 Binomial Probability Distributions 4-4 Mean, Variance, and Standard Deviation for the Binomial Distribution 4-5 The Poisson Distribution
MATH 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
CHAPTER 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
Statistical Methods in Practice STAT/MATH 3379
Statistical Methods in Practice STAT/MATH 3379 Dr. A. B. W. Manage Associate Professor of Mathematics & Statistics Department of Mathematics & Statistics Sam Houston State University Overview 6.1 Discrete
Example. 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
Lesson 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
Opening 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
Mathematics General 2
07 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics General General Instructions Reading time 5 minutes Working time hours Write using black pen NESA approved calculators may be used A formulae and data
Math489/889 Stochastic Processes and Advanced Mathematical Finance Homework 5
Math489/889 Stochastic Processes and Advanced Mathematical Finance Homework 5 Steve Dunbar Due Fri, October 9, 7. Calculate the m.g.f. of the random variable with uniform distribution on [, ] and then
Fall 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
THE UNITED REPUBLIC OF TANZANIA NATIONAL EXAMINATIONS COUNCIL CERTIFICATE OF SECONDARY EDUCATION EXAMINATION. Instructions
THE UNITED REPUBLIC OF TANZANIA NATIONAL EXAMINATIONS COUNCIL CERTIFICATE OF SECONDARY EDUCATION EXAMINATION 041 BASIC MATHEMATICS (For School Candidates Only) Time: 3 Hours Tuesday, 05 th November 2013
What is the probability of success? Failure? How could we do this simulation using a random number table?
Probability Ch.4, sections 4.2 & 4.3 Binomial and Geometric Distributions Name: Date: Pd: 4.2. What is a binomial distribution? How do we find the probability of success? Suppose you have three daughters.
Introduction to Business Statistics QM 120 Chapter 6
DEPARTMENT OF QUANTITATIVE METHODS & INFORMATION SYSTEMS Introduction to Business Statistics QM 120 Chapter 6 Spring 2008 Chapter 6: Continuous Probability Distribution 2 When a RV x is discrete, we can
(Practice Version) Midterm Exam 1
EECS 126 Probability and Random Processes University of California, Berkeley: Fall 2014 Kannan Ramchandran September 19, 2014 (Practice Version) Midterm Exam 1 Last name First name SID Rules. DO NOT open
Binomial Distributions
. Binomial Distributions Essential Question How can you determine the frequency of each outcome of an event? Analyzing Histograms Work with a partner. The histograms show the results when n coins are flipped.
Chapter 8. Variables. Copyright 2004 Brooks/Cole, a division of Thomson Learning, Inc.
Chapter 8 Random Variables Copyright 2004 Brooks/Cole, a division of Thomson Learning, Inc. 8.1 What is a Random Variable? Random Variable: assigns a number to each outcome of a random circumstance, or,
MATH 218 FINAL EXAMINATION December 17, 2003 Professors: J. Colwell, F. Lin, K. Styrkas, E. Verona, Z. Vorel.
MATH 218 FINAL EXAMINATION December 17, 2003 Professors: J. Colwell, F. Lin, K. Styrkas, E. Verona, Z. Vorel. Problem 1. A random sample of 50 purchases at a department store produced the following contingency
Examples: Random Variables. Discrete and Continuous Random Variables. Probability Distributions
Random Variables Examples: Random variable a variable (typically represented by x) that takes a numerical value by chance. Number of boys in a randomly selected family with three children. Possible values:
List of Online Quizzes: Quiz7: Basic Probability Quiz 8: Expectation and sigma. Quiz 9: Binomial Introduction Quiz 10: Binomial Probability
List of Online Homework: Homework 6: Random Variables and Discrete Variables Homework7: Expected Value and Standard Dev of a Variable Homework8: The Binomial Distribution List of Online Quizzes: Quiz7:
Test - Sections 11-13
Test - Sections 11-13 version 1 You have just been offered a job with medical benefits. In talking with the insurance salesperson you learn that the insurer uses the following probability calculations:
Chapter 5. Discrete Probability Distributions. McGraw-Hill, Bluman, 7 th ed, Chapter 5 1
Chapter 5 Discrete Probability Distributions McGraw-Hill, Bluman, 7 th ed, Chapter 5 1 Chapter 5 Overview Introduction 5-1 Probability Distributions 5-2 Mean, Variance, Standard Deviation, and Expectation
Math 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
Stat3011: Solution of Midterm Exam One
1 Stat3011: Solution of Midterm Exam One Fall/2003, Tiefeng Jiang Name: Problem 1 (30 points). Choose one appropriate answer in each of the following questions. 1. (B ) The mean age of five people in a
Math : Spring 2008
Math 1070-2: Spring 2008 Lecture 7 Davar Khoshnevisan Department of Mathematics University of Utah http://www.math.utah.edu/ davar February 27, 2008 An example A WHO study of health: In Canada, the systolic
Example - 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
HHH 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
Supplementary Material to: Peer Effects, Teacher Incentives, and the Impact of Tracking: Evidence from a Randomized Evaluation in Kenya
Supplementary Material to: Peer Effects, Teacher Incentives, and the Impact of Tracking: Evidence from a Randomized Evaluation in Kenya by Esther Duflo, Pascaline Dupas, and Michael Kremer This document
Value (x) probability Example A-2: Construct a histogram for population Ψ.
Calculus 111, section 08.x The Central Limit Theorem notes by Tim Pilachowski If you haven t done it yet, go to the Math 111 page and download the handout: Central Limit Theorem supplement. Today s lecture
Problem Set 07 Discrete Random Variables
Name Problem Set 07 Discrete Random Variables MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the mean of the random variable. 1) The random
Probability and Sample space
Probability and Sample space We call a phenomenon random if individual outcomes are uncertain but there is a regular distribution of outcomes in a large number of repetitions. The probability of any outcome
AVERAGE. Example1: Find an average of following observations: 3, 4, 8, 12, 2, 5, 1. Sum of all observations
Bank AVERAGE Average is a very simple topic and just involves simple mathematical calculations. Average concept has various applications. We will discuss its applications in next session. Firstly we will
Name: Show all your work! Mathematical Concepts Joysheet 1 MAT 117, Spring 2012 D. Ivanšić
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
Math 227 (Statistics) Chapter 6 Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Math 227 (Statistics) Chapter 6 Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Using the following uniform density curve, answer the
23.1 Probability Distributions
3.1 Probability Distributions Essential Question: What is a probability distribution for a discrete random variable, and how can it be displayed? Explore Using Simulation to Obtain an Empirical Probability
Part 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
Name: 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
Discrete Probability Distributions
Discrete Probability Distributions Chapter 6 Copyright 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. Learning
ECON 214 Elements of Statistics for Economists
ECON 214 Elements of Statistics for Economists Session 7 The Normal Distribution Part 1 Lecturer: Dr. Bernardin Senadza, Dept. of Economics Contact Information: bsenadza@ug.edu.gh College of Education
Probability Distributions. Chapter 6
Probability Distributions Chapter 6 McGraw-Hill/Irwin The McGraw-Hill Companies, Inc. 2008 GOALS Define the terms probability distribution and random variable. Distinguish between discrete and continuous
4.1 Probability Distributions
Probability and Statistics Mrs. Leahy Chapter 4: Discrete Probability Distribution ALWAYS KEEP IN MIND: The Probability of an event is ALWAYS between: and!!!! 4.1 Probability Distributions Random Variables
Determine whether the given events are disjoint. 1) Drawing a face card from a deck of cards and drawing a deuce A) Yes B) No
Assignment 8.-8.6 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the given events are disjoint. 1) Drawing a face card from
Chapter 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.
Probability. An intro for calculus students P= Figure 1: A normal integral
Probability An intro for calculus students.8.6.4.2 P=.87 2 3 4 Figure : A normal integral Suppose we flip a coin 2 times; what is the probability that we get more than 2 heads? Suppose we roll a six-sided
Central Limit Theorem 11/08/2005
Central Limit Theorem 11/08/2005 A More General Central Limit Theorem Theorem. Let X 1, X 2,..., X n,... be a sequence of independent discrete random variables, and let S n = X 1 + X 2 + + X n. For each
Diploma in Financial Management with Public Finance
Diploma in Financial Management with Public Finance Cohort: DFM/09/FT Jan Intake Examinations for 2009 Semester II MODULE: STATISTICS FOR FINANCE MODULE CODE: QUAN 1103 Duration: 2 Hours Reading time:
SECTION 4.4: Expected Value
15 SECTION 4.4: Expected Value This section tells you why most all gambling is a bad idea. And also why carnival or amusement park games are a bad idea. Random Variables Definition: Random Variable A random
3. Flip two pennies, and record the number of heads observed. Repeat this chance experiment three more times for a total of four flips.
Student Outcomes Given a description of a discrete random variable, students determine the probability distribution of that variable. Students interpret probabilities in context. Lesson Notes In this lesson,