Chapter 3 – Discrete Random Variables and Probability

Distributions

Outline – Random variables

Outline – Discrete random variables and distributions

Outline – Expected values of discrete random variables

Outline – Binomial probability distribution

Outline – Hypergeometric and negative binomial distributions

Outline – Poisson probability distribution

Random Variables

Discrete random variables

Continuous random variables

Probability mass function

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 binomial distributions

Calculations with binomial distributions (cont’d)

pmf of binomial

cdf of binomial

Sampling with or without replacement

Hypergeometric distribution

Properties and Examples

Approximation of hypergeometric by binomial

Negative Binomial

Negative Binomial (cont’d)

Poisson distribution

Approximating binomials

Comparison plot of binomial and Poisson approximation

Poisson process