Suppose N1is a discrete random variable equally likely to take on any integer in the set {1, 2, 3}. Given that, N1 = n1, the random variable N2 is equally likely to take on any integer in the set {1, 2… n2}. Finally, given that N2 = n2, the random variable is equally likely to take on any integer in the set {1, 2… n2}.
(a) Find the two- dimensional joint PMF, P N1, N2 (n1, n2).
(b) Find the three- dimensional joint PDF, PN1, N2, N3 (n1, n2, n3).
(c) Find the marginal PDFs, PN2 (n2) and PN3 (n3).