The joint probability function of 2 discrete RVs X and Y is given by
PX,Y(x,y) = k(2x+y) x=1,2 ; y=1,2
= 0 otherwise
where k is a constant.
a) Find the value of k
b) Find the marginal probability functions of X and Y.
c) Are X and Y independent?
d) Compute the conditional probability function of Y given x = 2
e) Find the mean and the variance of X and Y
f) Find the correlation coefficient of X and Y
Please show all work and extra karma will be awarded for multiple parts (just post each section with work)