2. The joint PMF of a bivariate RV (X, Y) is given by p(x, y) = [k(2x+y), x= 1,2; y = 1, 2 10, otherwise where k is a constant. Find (a) the value of k, (b) the marginal PMF's of X and Y. (c) Are X and Y independent? (d) Find the

A First Course in Probability (10th Edition)
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2. The joint PMF of a bivariate RV (X, Y) is given by
p(x, y):
[k(2x+y), x= 1,2; y = 1, 2
10,
otherwise
where k is a constant.
Find (a) the value of k, (b) the marginal PMF's of X and Y. (c) Are X and Y independent? (d) Find the
conditional PMF's Pyx (yx) and Pxy(x|y) (e) Find P(Y = 2|X = 2) and P(X= 2|Y = 2).
Transcribed Image Text:2. The joint PMF of a bivariate RV (X, Y) is given by p(x, y): [k(2x+y), x= 1,2; y = 1, 2 10, otherwise where k is a constant. Find (a) the value of k, (b) the marginal PMF's of X and Y. (c) Are X and Y independent? (d) Find the conditional PMF's Pyx (yx) and Pxy(x|y) (e) Find P(Y = 2|X = 2) and P(X= 2|Y = 2).
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