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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