Joint and Conditional Distributions
Learning Objectives
- Explain what is meant by jointly distributed random variables, marginal distributions and conditional distributions.
- Define the probability function/density function of a marginal distribution and of a conditional distribution.
- Specify the conditions under which random variables are independent.
- Define the expected value of a function of two jointly distributed random variables, the covariance and correlation coefficient between two variables, and calculate such quantities.
- Define the probability function/density function of the sum of two independent random variables as the convolution of two functions.
- Derive the mean and variance of linear combinations of random variables.
Theory
R Practice