Texts: Hi, Can you help me to solve this question? I need help. I don't know how to do that. Please do not chatgpt thanks!
Let (X, Y) be a random vector with joint PMF given by:
P(X = x, Y = y) =
1/((x + y)^2) if x ∈ {1,2,...}, y ∈ {2,3,...}
0 otherwise
(a) Verify that P(X, Y)(x, y) is a valid joint PMF.
(b) Find the marginal PMFs of X and Y. Hint: You can answer this question without doing any additional summations!
(c) Use your answer to part (b) to compute E[X] and E[Y]. Hint: You can answer this question without doing any additional summations!
(d) Compute E[XY]. Hint: You can answer this question without doing any additional summations! Just be sure to justify all of your work/steps.