Suppose random variables X and Y are conditionally independent given random variable Z, i.e. P(X, Y|Z) = P(X|Z)P(Y|Z). Show that : (a) P(Y|X, Z) = P(Y|Z). (b) P(X|Y, Z) = P(X|Z).

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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Suppose random variables X and Y are conditionally independent given random variable Z, i.e. P(X, Y|Z) = P(X|Z)P(Y|Z). Show that : (a) P(Y|X, Z) = P(Y|Z). (b) P(X|Y, Z) = P(X|Z).
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