Chapter 4 Continuous Random Variables and Probability ... · Chapter 4 - Continuous Random...
Transcript of Chapter 4 Continuous Random Variables and Probability ... · Chapter 4 - Continuous Random...
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