Gamma(alpha) Normal(mu,sig2) Uniform(a,b) 2.5
|
|
|
- Letitia Wells
- 6 years ago
- Views:
Transcription
1 1 c Stat Concept 1.0 a=0,b= Lognormal(a,b) a=0,b=.25 a=0,b=1 a=1,b=.25 a=1,b= Gamma(alpha) alpha=1 alpha=2 alpha=3 alpha= c=1 Weibull(c) c=4 c=3 c= Laplace(mu,sig2) mu=0,sig2=.25 mu=0,sig2=1 mu=-2,sig2=1 mu=2,sig2=1 mu=0,sig2= Normal(mu,sig2) N(0,4) N(0,.25) N(-1,1) N(0,1)N(1,1) Logistic(a,b) a=0,b=.5 a=-2,b=1 a=0,b=1 a=2,b=1 a=0,b= Beta(p,q) 7 6 Beta(p=.5,q=.5) 5 4 Beta(p=2,q=9) Beta(p=9,q=2) 3 2 Beta(3,3) Uniform(a,b) U(-.25,.25) U(-.75,75) U(0,1) U(-2,2) Pareto(a) 4 a=4 3 a=3 2 a=2 1 a=
2 2
3 : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2.4 3
4 4
5 15.0/96,0/95,0/15,0/ : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : " ' " ' : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Z : : : : : : : : : : : : : : X : : : : : : : 3.4 5
6 6. :,.,,!,... CD,. ( ) StatConcept., " '. f :.
7 7..., S-PLUS ( CD).. 1 Stata.. 2 S-PLUS,. STEPS... f. ( ) ),,,, ( ) Newton, H.J. and Harvill, J.L. (1997) StatConcepts: A Visual Tour of Statistical Ideas. Duxbury Press: Pacic Grove, CA. 1 Data 2
8 8. Stat Concept ( src@src.ac.ir adel@aut.ac.ir mohammadpour_adel@yahoo.com b, f.....,..! 52,
9 1 : " ' , 4 3. f. 5 ) 8 ( 7 ) 6,. ( N. N. x N+1 = x 1 x N+2 = x 2. f Probability 1 Relative Frequency 2 Observations 3 Random Variables 4 Distributions 5 Simulation 6 Statistical Simulation 7 Psedo Random Number 8 Seed 9
10 .1 10 f ( ). ( ) Time f. 10 Introduction to Concept Labs,.. :. f ",.,..,.. 10
11 11?, , : (. ). 100
12 .1 12
13 2 1.2,. 1 4, Sample 1 Independent 2 Identicall 3 Independence 4
14 .2 14? 6 5 (1 7 '. " ' "? 8 (2.? (3., (4?? (5?? (6? (7. 3 (8 1.2 (9? 5 (1.2 ) 9 Random Sampling " (10. Population 5 Finite 6 Simple Random Sample 7 Innite 8 9
15 Random Sampling Yellow boxes contain average of 5 values from horizontal axis corresponding to most recently selected individuals. Red indices inside boxes represent labels of individuals in the population /96,0/95,0/15,0/05 :1.2 ( 11 ) 10? " (11?? b " (12 25,Random Sampling : ) (., 12 " (13.? b " (14? (15., (16 Pribability MassFunction 10 Density 11 Relative Frequence Table 12
16 .2 16 ndraws = 1, npairs = 1, relative frequency = :2.2 50? (2.2 ) 13 Relative Frequency and Probability " (17. 13
17 Theoretical (blue) and Observed (red) Histograms for a Discrete Probability Distribution (Chi-sq = p-value = ) :3.2 (3.2 ) 14 Sampling from Discrete Populations (18. 14
18 Sampling With (blue) and Without (red) Replacement (N = 50, n = 10 pi = 0.5 ) " ' " ' :4.2 (19 Sampling from 0-1 Population > Sampling With and Without Replacment (4.2 ) ( ). :?! :! With Replacement 15 Without Replacement 16 Binomial 17 Hypergeometric 18
19 3 1.3,,.,,,. 1 ( 2 ),,, 3., 19 Empirical Density Function 1 Histogram 2 Normal 3
20 (1.3 ) 4 How arepopulation Distributed (1 f.? " (2 ) Lab Option Simulated Data,, ( ).(2.3?. 4
21 Five Members of the Normal Family N(0,.25) N(-1,1) N(0,1) N(1,1) N(0,4) :1.3 Simulated Data from Normal (mean = 100, variance = 225) (Any data outside x range are in end boxes) 3 m1 = m2 = m3 = m4 = e5 Skewness = Kurtosis = :2.3
22 .3 22 " (3., " (4, ( ).., " (5 ( ). Lab Option Simulated Data " ( ( )?? (3.3 ) 5 Z, t, Chi-Square, F (7.,..,, f. ( )...!!... 5
23 Chi Square Curves :3.3
24 .3 24
25 ,,. 3, Statistic 1 Parameter 2 Sampling Distribution 3 Weak Law of Large Number 4 Central Limit Theorem 5
26 p 6 2 X 2 X 1 (1 X 2 X 1 x 2 x 1? T = X 1 + X 2? p t = x 1 + x 2 2 X 2 X 1 (2? X = 1 2 (X 1 + X 2 ) 2? 2 Random Sampling (3. 7? ( 20 f ) ) 2 2. (...., )? (., 5 f " (4? b 3 (5. 3. Bernoli 6 Mean 7
27 b Random Sampling ( b ( ) 1 : " (7 X.,... X.,.... (8., (1.4 ) 8 Sampling Distributions (9 Z = X q ; E(X) V (X) E(1) U(0 1),N(0 1) ( ) 500,n = 20 f n. z = 20 x; 8
28 Theoretical Distribution and Histogram of 500 Z Statistics Sampling from Normal(0,1), n = 5 Refer to the Report Window for numerical comparisons of the theoretical and Monte Carlo distributions Z :1.4 ).?,(?.?? (10.,(2.4 ) 9 Central Limit Theorom! (11 )? 9
29 Histogram of Sample Means of 500 Samples of Size 10 From Normal(0,1) Parent Population With Normal Theory Curve Superimposed X :2.4.( b? Z (12. (13. (14.? (15 ". X n '? (16 n?,n (17? 30 f
30 .4 30? ( ) (18 ( b b ).?. (19. P (0=001) 10 X 1 X 100 (a) P ( P 100 i=1 X i > 0). P (2) Y (b). P (Y > 0)?. (20. Statistical Tables. B(1 0=1) X 1 X 10 (a). P ( P 10 i=1 X i 2) B(1 0=3) X 1 X 10 (b). P ( P 10 i=1 X i 2). B(1 0=5) X 1 X 10 (c). P ( P 10 i=1 X i 2) (21 Sampling from 0- )??,(3.4 ) 1Population > Approximating Binomial Probabilities (.,." ' :!?, :? p X, X 2 n :,j n j' :, p X n "! Poisson 10
31 Poisson Approximation (red) to Binomial (blue) n = 50, pi = P(X= 4 ): Approximating B(n,pi) by N(n*pi, n*pi*(1-pi)) n = 10, pi = By bar: Under curve: :3.4
4-2 Probability Distributions and Probability Density Functions. Figure 4-2 Probability determined from the area under f(x).
4-2 Probability Distributions and Probability Density Functions Figure 4-2 Probability determined from the area under f(x). 4-2 Probability Distributions and Probability Density Functions Definition 4-2
Unit 5: Sampling Distributions of Statistics
Unit 5: Sampling Distributions of Statistics Statistics 571: Statistical Methods Ramón V. León 6/12/2004 Unit 5 - Stat 571 - Ramon V. Leon 1 Definitions and Key Concepts A sample statistic used to estimate
Unit 5: Sampling Distributions of Statistics
Unit 5: Sampling Distributions of Statistics Statistics 571: Statistical Methods Ramón V. León 6/12/2004 Unit 5 - Stat 571 - Ramon V. Leon 1 Definitions and Key Concepts A sample statistic used to estimate
Sampling Distribution of and Simulation Methods. Ontario Public Sector Salaries. Strange Sample? Lecture 11. Reading: Sections
Sampling Distribution of and Simulation Methods Lecture 11 Reading: Sections 1.3 1.5 1 Ontario Public Sector Salaries Public Sector Salary Disclosure Act, 1996 Requires organizations that receive public
Subject CS1 Actuarial Statistics 1 Core Principles. Syllabus. for the 2019 exams. 1 June 2018
` Subject CS1 Actuarial Statistics 1 Core Principles Syllabus for the 2019 exams 1 June 2018 Copyright in this Core Reading is the property of the Institute and Faculty of Actuaries who are the sole distributors.
2011 Pearson Education, Inc
Statistics for Business and Economics Chapter 4 Random Variables & Probability Distributions Content 1. Two Types of Random Variables 2. Probability Distributions for Discrete Random Variables 3. The Binomial
TOPIC: PROBABILITY DISTRIBUTIONS
TOPIC: PROBABILITY DISTRIBUTIONS There are two types of random variables: A Discrete random variable can take on only specified, distinct values. A Continuous random variable can take on any value within
Using Fat Tails to Model Gray Swans
Using Fat Tails to Model Gray Swans Paul D. Kaplan, Ph.D., CFA Vice President, Quantitative Research Morningstar, Inc. 2008 Morningstar, Inc. All rights reserved. Swans: White, Black, & Gray The Black
ก ก ก ก ก ก ก. ก (Food Safety Risk Assessment Workshop) 1 : Fundamental ( ก ( NAC 2010)) 2 3 : Excel and Statistics Simulation Software\
![ก ก ก ก ก ก ก. ก (Food Safety Risk Assessment Workshop) 1 : Fundamental ( ก ( NAC 2010)) 2 3 : Excel and Statistics Simulation Software\](/thumbs/96/127772311.jpg "ก ก ก ก ก ก ก. ก (Food Safety Risk Assessment Workshop) 1 : Fundamental ( ก ( NAC 2010)) 2 3 : Excel and Statistics Simulation Software\")
ก ก ก ก (Food Safety Risk Assessment Workshop) ก ก ก ก ก ก ก ก 5 1 : Fundamental ( ก 29-30.. 53 ( NAC 2010)) 2 3 : Excel and Statistics Simulation Software\ 1 4 2553 4 5 : Quantitative Risk Modeling Microbial
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
Lean Six Sigma: Training/Certification Books and Resources
Lean Si Sigma Training/Certification Books and Resources Samples from MINITAB BOOK Quality and Si Sigma Tools using MINITAB Statistical Software A complete Guide to Si Sigma DMAIC Tools using MINITAB Prof.
Chapter 7: Point Estimation and Sampling Distributions
Chapter 7: Point Estimation and Sampling Distributions Seungchul Baek Department of Statistics, University of South Carolina STAT 509: Statistics for Engineers 1 / 20 Motivation In chapter 3, we learned
Monte Carlo Simulation (General Simulation Models)
Monte Carlo Simulation (General Simulation Models) Revised: 10/11/2017 Summary... 1 Example #1... 1 Example #2... 10 Summary Monte Carlo simulation is used to estimate the distribution of variables when
Model 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
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
Discrete Random Variables
Discrete Random Variables In this chapter, we introduce a new concept that of a random variable or RV. A random variable is a model to help us describe the state of the world around us. Roughly, a RV can
Chapter 4. The Normal Distribution
Chapter 4 The Normal Distribution 1 Chapter 4 Overview Introduction 4-1 Normal Distributions 4-2 Applications of the Normal Distribution 4-3 The Central Limit Theorem 4-4 The Normal Approximation to the
Chapter 3 Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2013 John Wiley & Sons, Inc.
1 3.1 Describing Variation Stem-and-Leaf Display Easy to find percentiles of the data; see page 69 2 Plot of Data in Time Order Marginal plot produced by MINITAB Also called a run chart 3 Histograms Useful
10-3 Probability Distributions
Identify the random variable in each distribution, and classify it as discrete or continuous. Explain your reasoning. 1. the number of pages linked to a Web page The random variable X is the number of
UQ, STAT2201, 2017, Lectures 3 and 4 Unit 3 Probability Distributions.
UQ, STAT2201, 2017, Lectures 3 and 4 Unit 3 Probability Distributions. Random Variables 2 A random variable X is a numerical (integer, real, complex, vector etc.) summary of the outcome of the random experiment.
Discrete Probability Distributions
90 Discrete Probability Distributions Discrete Probability Distributions C H A P T E R 6 Section 6.2 4Example 2 (pg. 00) Constructing a Binomial Probability Distribution In this example, 6% of the human
ME3620. Theory of Engineering Experimentation. Spring Chapter III. Random Variables and Probability Distributions.
ME3620 Theory of Engineering Experimentation Chapter III. Random Variables and Probability Distributions Chapter III 1 3.2 Random Variables In an experiment, a measurement is usually denoted by a variable
Contents Part I Descriptive Statistics 1 Introduction and Framework Population, Sample, and Observations Variables Quali
Part I Descriptive Statistics 1 Introduction and Framework... 3 1.1 Population, Sample, and Observations... 3 1.2 Variables.... 4 1.2.1 Qualitative and Quantitative Variables.... 5 1.2.2 Discrete and Continuous
Chapter 6 Part 3 October 21, Bootstrapping
Chapter 6 Part 3 October 21, 2008 Bootstrapping From the internet: The bootstrap involves repeated re-estimation of a parameter using random samples with replacement from the original data. Because the
Section The Sampling Distribution of a Sample Mean
Section 5.2 - The Sampling Distribution of a Sample Mean Statistics 104 Autumn 2004 Copyright c 2004 by Mark E. Irwin The Sampling Distribution of a Sample Mean Example: Quality control check of light
Market Risk Analysis Volume I
Market Risk Analysis Volume I Quantitative Methods in Finance Carol Alexander John Wiley & Sons, Ltd List of Figures List of Tables List of Examples Foreword Preface to Volume I xiii xvi xvii xix xxiii
STAT Chapter 5: Continuous Distributions. Probability distributions are used a bit differently for continuous r.v. s than for discrete r.v. s.
STAT 515 -- Chapter 5: Continuous Distributions Probability distributions are used a bit differently for continuous r.v. s than for discrete r.v. s. Continuous distributions typically are represented by
Probability and Statistics
Kristel Van Steen, PhD 2 Montefiore Institute - Systems and Modeling GIGA - Bioinformatics ULg kristel.vansteen@ulg.ac.be CHAPTER 3: PARAMETRIC FAMILIES OF UNIVARIATE DISTRIBUTIONS 1 Why do we need distributions?
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
Chapter 4 Random Variables & Probability. Chapter 4.5, 6, 8 Probability Distributions for Continuous Random Variables
Chapter 4.5, 6, 8 Probability for Continuous Random Variables Discrete vs. continuous random variables Examples of continuous distributions o Uniform o Exponential o Normal Recall: A random variable =
Computational Statistics Handbook with MATLAB
«H Computer Science and Data Analysis Series Computational Statistics Handbook with MATLAB Second Edition Wendy L. Martinez The Office of Naval Research Arlington, Virginia, U.S.A. Angel R. Martinez Naval
Math 227 Elementary Statistics. Bluman 5 th edition
Math 227 Elementary Statistics Bluman 5 th edition CHAPTER 6 The Normal Distribution 2 Objectives Identify distributions as symmetrical or skewed. Identify the properties of the normal distribution. Find
QQ PLOT Yunsi Wang, Tyler Steele, Eva Zhang Spring 2016
QQ PLOT INTERPRETATION: Quantiles: QQ PLOT Yunsi Wang, Tyler Steele, Eva Zhang Spring 2016 The quantiles are values dividing a probability distribution into equal intervals, with every interval having
PROBABILITY. Wiley. With Applications and R ROBERT P. DOBROW. Department of Mathematics. Carleton College Northfield, MN
PROBABILITY With Applications and R ROBERT P. DOBROW Department of Mathematics Carleton College Northfield, MN Wiley CONTENTS Preface Acknowledgments Introduction xi xiv xv 1 First Principles 1 1.1 Random
Business Statistics 41000: Probability 4
Business Statistics 41000: Probability 4 Drew D. Creal University of Chicago, Booth School of Business February 14 and 15, 2014 1 Class information Drew D. Creal Email: dcreal@chicagobooth.edu Office:
Module 3: Sampling Distributions and the CLT Statistics (OA3102)
Module 3: Sampling Distributions and the CLT Statistics (OA3102) Professor Ron Fricker Naval Postgraduate School Monterey, California Reading assignment: WM&S chpt 7.1-7.3, 7.5 Revision: 1-12 1 Goals for
1/2 2. Mean & variance. Mean & standard deviation
Question # 1 of 10 ( Start time: 09:46:03 PM ) Total Marks: 1 The probability distribution of X is given below. x: 0 1 2 3 4 p(x): 0.73? 0.06 0.04 0.01 What is the value of missing probability? 0.54 0.16
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
ELEMENTS OF MONTE CARLO SIMULATION
APPENDIX B ELEMENTS OF MONTE CARLO SIMULATION B. GENERAL CONCEPT The basic idea of Monte Carlo simulation is to create a series of experimental samples using a random number sequence. According to the
Session Window. Variable Name Row. Worksheet Window. Double click on MINITAB icon. You will see a split screen: Getting Started with MINITAB
STARTING MINITAB: Double click on MINITAB icon. You will see a split screen: Session Window Worksheet Window Variable Name Row ACTIVE WINDOW = BLUE INACTIVE WINDOW = GRAY f(x) F(x) Getting Started with
Contents. An Overview of Statistical Applications CHAPTER 1. Contents (ix) Preface... (vii)
Contents (ix) Contents Preface... (vii) CHAPTER 1 An Overview of Statistical Applications 1.1 Introduction... 1 1. Probability Functions and Statistics... 1..1 Discrete versus Continuous Functions... 1..
CH 5 Normal Probability Distributions Properties of the Normal Distribution
Properties of the Normal Distribution Example A friend that is always late. Let X represent the amount of minutes that pass from the moment you are suppose to meet your friend until the moment your friend
Fitting parametric distributions using R: the fitdistrplus package
Fitting parametric distributions using R: the fitdistrplus package M. L. Delignette-Muller - CNRS UMR 5558 R. Pouillot J.-B. Denis - INRA MIAJ user! 2009,10/07/2009 Background Specifying the probability
Probability Models.S2 Discrete Random Variables
Probability Models.S2 Discrete Random Variables Operations Research Models and Methods Paul A. Jensen and Jonathan F. Bard Results of an experiment involving uncertainty are described by one or more random
CS 237: Probability in Computing
CS 237: Probability in Computing Wayne Snyder Computer Science Department Boston University Lecture 12: Continuous Distributions Uniform Distribution Normal Distribution (motivation) Discrete vs Continuous
Central University of Punjab, Bathinda
P a g e 1 Central University of Punjab, Bathinda Course Scheme & Syllabus for University Statistics P a g e 1 Sr. No. Course Code 1 TBA1 2 TBA2 3 TBA3 Course Title Basic Statistics (Sciences) Basic Statistics
Basic 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
Counting 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
LAB 2 INSTRUCTIONS PROBABILITY DISTRIBUTIONS IN EXCEL
LAB 2 INSTRUCTIONS PROBABILITY DISTRIBUTIONS IN EXCEL There is a wide range of probability distributions (both discrete and continuous) available in Excel. They can be accessed through the Insert Function
Simulation of Moment, Cumulant, Kurtosis and the Characteristics Function of Dagum Distribution
264 Simulation of Moment, Cumulant, Kurtosis and the Characteristics Function of Dagum Distribution Dian Kurniasari 1*,Yucky Anggun Anggrainy 1, Warsono 1, Warsito 2 and Mustofa Usman 1 1 Department of
Chapter 7 Sampling Distributions and Point Estimation of Parameters
Chapter 7 Sampling Distributions and Point Estimation of Parameters Part 1: Sampling Distributions, the Central Limit Theorem, Point Estimation & Estimators Sections 7-1 to 7-2 1 / 25 Statistical Inferences
MLLunsford 1. Activity: Central Limit Theorem Theory and Computations
MLLunsford 1 Activity: Central Limit Theorem Theory and Computations Concepts: The Central Limit Theorem; computations using the Central Limit Theorem. Prerequisites: The student should be familiar with
Monte Carlo Simulation (Random Number Generation)
Monte Carlo Simulation (Random Number Generation) Revised: 10/11/2017 Summary... 1 Data Input... 1 Analysis Options... 6 Summary Statistics... 6 Box-and-Whisker Plots... 7 Percentiles... 9 Quantile Plots...
Introduction to Statistics I
Introduction to Statistics I Keio University, Faculty of Economics Continuous random variables Simon Clinet (Keio University) Intro to Stats November 1, 2018 1 / 18 Definition (Continuous random variable)
Business Statistics 41000: Probability 3
Business Statistics 41000: Probability 3 Drew D. Creal University of Chicago, Booth School of Business February 7 and 8, 2014 1 Class information Drew D. Creal Email: dcreal@chicagobooth.edu Office: 404
Central Limit Theorem (CLT) RLS
Central Limit Theorem (CLT) RLS Central Limit Theorem (CLT) Definition The sampling distribution of the sample mean is approximately normal with mean µ and standard deviation (of the sampling distribution
About the Risk Quantification of Technical Systems
About the Risk Quantification of Technical Systems Magda Schiegl ASTIN Colloquium 2013, The Hague Outline Introduction / Overview Fault Tree Analysis (FTA) Method of quantitative risk analysis Results
Data Analytics (CS40003) Practice Set IV (Topic: Probability and Sampling Distribution)
Data Analytics (CS40003) Practice Set IV (Topic: Probability and Sampling Distribution) I. Concept Questions 1. Give an example of a random variable in the context of Drawing a card from a deck of cards.
Part 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.
Probability and Statistics for Engineers
Probability and Statistics for Engineers Chapter 4 Probability Distributions ruochen Liu ruochenliu@xidian.edu.cn Institute of Intelligent Information Processing, Xidian University Outline Random variables
Statistics 511 Additional Materials
Discrete Random Variables In this section, we introduce the concept of a random variable or RV. A random variable is a model to help us describe the state of the world around us. Roughly, a RV can be thought
XLSTAT TIP SHEET FOR BUSINESS STATISTICS CENGAGE LEARNING
XLSTAT TIP SHEET FOR BUSINESS STATISTICS CENGAGE LEARNING INTRODUCTION XLSTAT makes accessible to anyone a powerful, complete and user-friendly data analysis and statistical solution. Accessibility to
A First Course in Probability
A First Course in Probability Seventh Edition Sheldon Ross University of Southern California PEARSON Prentice Hall Upper Saddle River, New Jersey 07458 Preface 1 Combinatorial Analysis 1 1.1 Introduction
Probability Distribution Unit Review
Probability Distribution Unit Review Topics: Pascal's Triangle and Binomial Theorem Probability Distributions and Histograms Expected Values, Fair Games of chance Binomial Distributions Hypergeometric
2017 Fall QMS102 Tip Sheet 2
Chapter 5: Basic Probability 2017 Fall QMS102 Tip Sheet 2 (Covering Chapters 5 to 8) EVENTS -- Each possible outcome of a variable is an event, including 3 types. 1. Simple event = Described by a single
Section 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
Data Science Essentials
Data Science Essentials Probability and Random Variables As data scientists, we re often concerned with understanding the qualities and relationships of a set of data points. For example, you may need
Commonly Used Distributions
Chapter 4: Commonly Used Distributions 1 Introduction Statistical inference involves drawing a sample from a population and analyzing the sample data to learn about the population. We often have some knowledge
M249 Diagnostic Quiz
THE OPEN UNIVERSITY Faculty of Mathematics and Computing M249 Diagnostic Quiz Prepared by the Course Team [Press to begin] c 2005, 2006 The Open University Last Revision Date: May 19, 2006 Version 4.2
Basic Principles of Probability and Statistics. Lecture notes for PET 472 Spring 2012 Prepared by: Thomas W. Engler, Ph.D., P.E
Basic Principles of Probability and Statistics Lecture notes for PET 472 Spring 2012 Prepared by: Thomas W. Engler, Ph.D., P.E Definitions Risk Analysis Assessing probabilities of occurrence for each possible
3. Probability Distributions and Sampling
3. Probability Distributions and Sampling 3.1 Introduction: the US Presidential Race Appendix 2 shows a page from the Gallup WWW site. As you probably know, Gallup is an opinion poll company. The page
Lecture Slides. Elementary Statistics Tenth Edition. by Mario F. Triola. and the Triola Statistics Series. Slide 1
Lecture Slides Elementary Statistics Tenth Edition and the Triola Statistics Series by Mario F. Triola Slide 1 Chapter 6 Normal Probability Distributions 6-1 Overview 6-2 The Standard Normal Distribution
DESCRIBING DATA: MESURES OF LOCATION
DESCRIBING DATA: MESURES OF LOCATION A. Measures of Central Tendency Measures of Central Tendency are used to pinpoint the center or average of a data set which can then be used to represent the typical
Continuous random variables
Continuous random variables probability density function (f(x)) the probability distribution function of a continuous random variable (analogous to the probability mass function for a discrete random variable),
LOSS SEVERITY DISTRIBUTION ESTIMATION OF OPERATIONAL RISK USING GAUSSIAN MIXTURE MODEL FOR LOSS DISTRIBUTION APPROACH
LOSS SEVERITY DISTRIBUTION ESTIMATION OF OPERATIONAL RISK USING GAUSSIAN MIXTURE MODEL FOR LOSS DISTRIBUTION APPROACH Seli Siti Sholihat 1 Hendri Murfi 2 1 Department of Accounting, Faculty of Economics,
Stat 213: Intro to Statistics 9 Central Limit Theorem
1 Stat 213: Intro to Statistics 9 Central Limit Theorem H. Kim Fall 2007 2 unknown parameters Example: A pollster is sure that the responses to his agree/disagree questions will follow a binomial distribution,
Basic Principles of Probability and Statistics. Lecture notes for PET 472 Spring 2010 Prepared by: Thomas W. Engler, Ph.D., P.E
Basic Principles of Probability and Statistics Lecture notes for PET 472 Spring 2010 Prepared by: Thomas W. Engler, Ph.D., P.E Definitions Risk Analysis Assessing probabilities of occurrence for each possible
Week 1 Variables: Exploration, Familiarisation and Description. Descriptive Statistics.
Week 1 Variables: Exploration, Familiarisation and Description. Descriptive Statistics. Convergent validity: the degree to which results/evidence from different tests/sources, converge on the same conclusion.
Statistical Tables Compiled by Alan J. Terry
Statistical Tables Compiled by Alan J. Terry School of Science and Sport University of the West of Scotland Paisley, Scotland Contents Table 1: Cumulative binomial probabilities Page 1 Table 2: Cumulative
ECO220Y Sampling Distributions of Sample Statistics: Sample Proportion Readings: Chapter 10, section
ECO220Y Sampling Distributions of Sample Statistics: Sample Proportion Readings: Chapter 10, section 10.1-10.3 Fall 2011 Lecture 9 (Fall 2011) Sampling Distributions Lecture 9 1 / 15 Sampling Distributions
Institute of Actuaries of India Subject CT6 Statistical Methods
Institute of Actuaries of India Subject CT6 Statistical Methods For 2014 Examinations Aim The aim of the Statistical Methods subject is to provide a further grounding in mathematical and statistical techniques
4: Probability. Notes: Range of possible probabilities: Probabilities can be no less than 0% and no more than 100% (of course).
4: Probability What is probability? The probability of an event is its relative frequency (proportion) in the population. An event that happens half the time (such as a head showing up on the flip of a
Section Random Variables and Histograms
Section 3.1 - Random Variables and Histograms Definition: A random variable is a rule that assigns a number to each outcome of an experiment. Example 1: Suppose we toss a coin three times. Then we could
Chapter 5: Statistical Inference (in General)
Chapter 5: Statistical Inference (in General) Shiwen Shen University of South Carolina 2016 Fall Section 003 1 / 17 Motivation In chapter 3, we learn the discrete probability distributions, including Bernoulli,
The histogram should resemble the uniform density, the mean should be close to 0.5, and the standard deviation should be close to 1/ 12 =
Chapter 19 Monte Carlo Valuation Question 19.1 The histogram should resemble the uniform density, the mean should be close to.5, and the standard deviation should be close to 1/ 1 =.887. Question 19. The
Data Analysis and Statistical Methods Statistics 651
Data Analysis and Statistical Methods Statistics 651 http://www.stat.tamu.edu/~suhasini/teaching.html Suhasini Subba Rao The binomial: mean and variance Recall that the number of successes out of n, denoted
KARACHI UNIVERSITY BUSINESS SCHOOL UNIVERSITY OF KARACHI BS (BBA) VI
88 P a g e B S ( B B A ) S y l l a b u s KARACHI UNIVERSITY BUSINESS SCHOOL UNIVERSITY OF KARACHI BS (BBA) VI Course Title : STATISTICS Course Number : BA(BS) 532 Credit Hours : 03 Course 1. Statistical
HANDBOOK OF. Market Risk CHRISTIAN SZYLAR WILEY
HANDBOOK OF Market Risk CHRISTIAN SZYLAR WILEY Contents FOREWORD ACKNOWLEDGMENTS ABOUT THE AUTHOR INTRODUCTION XV XVII XIX XXI 1 INTRODUCTION TO FINANCIAL MARKETS t 1.1 The Money Market 4 1.2 The Capital
12 Math Chapter Review April 16 th, Multiple Choice Identify the choice that best completes the statement or answers the question.
Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which situation does not describe a discrete random variable? A The number of cell phones per household.
Chapter 4: Commonly Used Distributions. Statistics for Engineers and Scientists Fourth Edition William Navidi
Chapter 4: Commonly Used Distributions Statistics for Engineers and Scientists Fourth Edition William Navidi 2014 by Education. This is proprietary material solely for authorized instructor use. Not authorized
Lecture 6: Chapter 6
Lecture 6: Chapter 6 C C Moxley UAB Mathematics 3 October 16 6.1 Continuous Probability Distributions Last week, we discussed the binomial probability distribution, which was discrete. 6.1 Continuous Probability
3.2 Binomial and Hypergeometric Probabilities
3.2 Binomial and Hypergeometric Probabilities Ulrich Hoensch Wednesday, January 23, 2013 Example An urn contains ten balls, exactly seven of which are red. Suppose five balls are drawn at random and with
Financial Models with Levy Processes and Volatility Clustering
Financial Models with Levy Processes and Volatility Clustering SVETLOZAR T. RACHEV # YOUNG SHIN ICIM MICHELE LEONARDO BIANCHI* FRANK J. FABOZZI WILEY John Wiley & Sons, Inc. Contents Preface About the
A probability distribution shows the possible outcomes of an experiment and the probability of each of these outcomes.
Introduction In the previous chapter we discussed the basic concepts of probability and described how the rules of addition and multiplication were used to compute probabilities. In this chapter we expand
Statistics 431 Spring 2007 P. Shaman. Preliminaries
Statistics 4 Spring 007 P. Shaman The Binomial Distribution Preliminaries A binomial experiment is defined by the following conditions: A sequence of n trials is conducted, with each trial having two possible
Chapter 7 1. Random Variables
Chapter 7 1 Random Variables random variable numerical variable whose value depends on the outcome of a chance experiment - discrete if its possible values are isolated points on a number line - continuous
Homework: Due Wed, Nov 3 rd Chapter 8, # 48a, 55c and 56 (count as 1), 67a
Homework: Due Wed, Nov 3 rd Chapter 8, # 48a, 55c and 56 (count as 1), 67a Announcements: There are some office hour changes for Nov 5, 8, 9 on website Week 5 quiz begins after class today and ends at
STAT Chapter 5: Continuous Distributions. Probability distributions are used a bit differently for continuous r.v. s than for discrete r.v. s.
STAT 515 -- Chapter 5: Continuous Distributions Probability distributions are used a bit differently for continuous r.v. s than for discrete r.v. s. Continuous distributions typically are represented by
Market Volatility and Risk Proxies
Market Volatility and Risk Proxies... an introduction to the concepts 019 Gary R. Evans. This slide set by Gary R. Evans is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International
AP STATISTICS FALL SEMESTSER FINAL EXAM STUDY GUIDE
AP STATISTICS Name: FALL SEMESTSER FINAL EXAM STUDY GUIDE Period: *Go over Vocabulary Notecards! *This is not a comprehensive review you still should look over your past notes, homework/practice, Quizzes,