Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete random variables, with joint PMF given by: SHOW SOLUTIONS X\Y 0 1 2 3 6 0 28 28 28 9 6 1 0 28 28 3 2 0 0 28

Determine E(x) and E(y)

We have the following information about the random variables X and Y: |x = 1, |y = −1.5 , ox = 0.25, c} = 1. o Calculate the variance of Z = 3X + 5Y, a) when the coefficient of correlation is p(X, Y) = 0.46: 0²77 34.15 Z b) when X and Y are independent random variables: 0²2 27.75 X

Consider the following joint random variable pmf for X and Y: x y   -1 0 1/4 0 1 1/8 1 1 1/2 1 0 1/8   What is the correlation of X and Y?