Page 1
Chapter 5: Joint Probability
Distributions
Page 2
Outline – Jointly Distributed
Random Variables
Page 3
Outline – Expected values,
covariance and correlation
Page 4
Outline – Statistics and their
distributions
Page 5
Outline – Distribution of the
Sample Mean
Page 6
Outline – The Distribution of
Linear Combinations
Page 7
Joint Probability Mass Function
Page 8
Joint Probability Density
Function
Page 9
Example of joint probability
density
Page 10
Marginal densities in example
Page 11
Independent Random Variables
Page 12
Conditional distributions
Page 15
Definition of a statistic
Page 17
Simulation experiments
Page 18
Steps in a simulation experiment
Page 19
Simulating a sample mean from a
Weibull
Page 20
Simulating a sample mean from a
Weibull (cont’d)
Page 21
Characteristics of the simulated
values
Page 22
Density plot and histogram
Page 23
Normal probability plot of
sample means
Page 24
Multiple sample sizes
Page 25
Histograms of means of different
sizes of samples
Page 26
Densities of means of different
sizes of samples
Page 27
Example 5.23 – Simulating from
a skew distribution
Page 29
Histograms of means from a log-
normal distribution
Page 30
Densities of means from a log-
normal distribution
Page 31
Properties of sample mean and
sample sum
Page 32
Central Limit Theorem
Page 33
Convergence of means from U[-
1,1] to a normal shape
Page 34
Histograms of raw means of
samples from U[-1,1].
Page 35
Densities of scaled means of
samples from U[-1,1].
Page 36
Linear Combinations and their
means
Page 37
Variances of linear combinations
Page 38
The difference between random
variables
Page 39
The Case of Normal Random
Variables