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

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

The Gamma distribution

Gamma density curves

Probabilities from the gamma distribution

The exponential distribution

Exponential density curves

The Chi-squared distribution

Chi-squared densities