In: Statistics and Probability
A multivariate random variable (X1, X2, X3) takes values in the following set S with equal probability: S = {(1, 1, 1),(3, 0, 0),(0, 3, 0),(0, 0, 3),(1, 2, 3)}.
a) Compute E[X1|X2 = i], for each i = 0, 1, 2, 3, and E[X1].
b) Compute the marginal p.m.f. of Xi for each i = 1, 2, 3.