The joint probability function of two discrete r.v's X and Y is given by f(x, y) = c(2x+y), where x and y can assume all integers such that 0 ≤ x ≤2,0 ≤ y ≤ 3 and f(x,y) =0 otherwise. Find E(X), E(Y) , E(XY), E($X^2$), E($Y^2$), var(X), var(Y), cov(X, Y) and ϱ.

X and Y are discrete RVs

To find c: We can tabulate the probabilities as follows:

$f(x,y)= c(2x+y)$         $0 ≤ x ≤ 2,0 ≤ y ≤ 3$

        =0