Expectation for Jointly Distributed Random Variables

Question

I just had a doubt about calculating the expectation of joint random vaiables.

Suppose we have a bivariate table such that: P(3,0) = a, P(1,2) = b, P(2,1) = c, P(0,3) = d

for P(x,y). So, when we calculate expectation of both x and y: would it be like: 1.2.b + 2.1.c and (we didn't take 'a' and 'd' cause it has 0 in multiplication)

Is this how we calculate expectation of joint rv's?

Answer 1

It looks like you are finding the expectation of $XY$. See this link for formulas: discrete probability formulas

In this case, $$E(X)=3a+1b+2c$$ $$E(Y)=2b+1c+3d$$