Chapter 4 – Continuous Random

Variables and Probability

Distributions

Outline – Continuous random

variables and probability density

functions

Outline – Cumulative distribution

function and expected values

Outline – The normal distribution

Outline – The Gamma

distribution and its relatives

Outline – Probability plots

Continuous Random Variables

Probability density function

Motivating probability density

function

Uniform distribution

Example 4.4

The cumulative distribution

function

Computing probabilities using

the cdf

Example 4.6

Percentiles of a continuous

distribution

Mean of a continuous random

variable

Example 4.9

Example 4.9 continued

Expected value of a function of a

rv

Example 4.10

Variance of a continuous rv

A shortcut formula for variance

The normal distribution

Normal density curves

The standard normal distribution

Nonstandard normal distribution

Percentiles of normal

distributions

Normal approximation to

binomial

The Gamma distribution

Gamma density curves

Probabilities from the gamma

distribution

The exponential distribution

Exponential density curves

The Chi-squared distribution

Chi-squared densities

Normal probability plot

Normal probability plot