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 (y|x) and Pxy (x|y) (e) Find P(Y = 2|X = 2) and P(X = 2|Y = 2).
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 (y|x) and Pxy (x|y) (e) Find P(Y = 2|X = 2) and P(X = 2|Y = 2).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Solve d and e part only
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 (y|x) and Pxy (x|y) (e) Find P(Y = 2|X = 2) and P(X = 2|Y = 2).
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