chapter 3 – discrete random variables and probability ... · variables and probability...

Chapter 3 – Discrete Random Variables and Probability

DistributionsDistributions

Outline – Random variables

Outline – Discrete randomOutline Discrete random variables and distributions

Outline – Expected values ofOutline Expected values of discrete random variables

Outline – Binomial probabilityOutline Binomial probability distribution

Outline – Hypergeometric andOutline Hypergeometric and negative binomial distributions

Outline – Poisson probabilityOutline Poisson probability distribution

Random Variables

Discrete random variables

Continuous random variables

Probability mass function

Plotting the pmf

Parameters of a distribution

Cumulative Distribution Function

CDF (cont’d)

Plot of CDF

Enhanced Plot of CDF

Plots from CDF’s defined in R

Expected value

Expected value of a function of x

Variance of a distribution

Binomial Probability Distribution

Binomial distribution in R

Calculations with binomialCalculations with binomial distributions

Calculations with binomialCalculations with binomial distributions (cont’d)

pmf of binomial

cdf of binomial

Sampling with or withoutSampling with or without replacement

Hypergeometric distribution

Properties and Examples

Approximation ofApproximation of hypergeometric by binomial

Negative Binomial

Negative Binomial (cont’d)

Poisson distribution

Approximating binomials

Comparison plot of binomial andComparison plot of binomial and Poisson approximation

Poisson process