# Slides from Lynne Butler’s Presentation on Joint Probability Distributions

Exercise: Use the joint distribution for the pair of random variables to calculate the expected value and variance of X and the expected value and variance of Y.

The random variables X and Y are not independent, because P(X=x and Y=y) does not equal P(X=x)P(Y=y). If X and Y had been independent, we would have found V(X+Y)=V(X)+V(Y). For independent random variables X and Y, Cov(X,Y)=0. In general, the covariance of X and Y is not zero. Above it is .05.