A random variable X~Binomial (2, 1/3) is chosen, but the result is badly recorded; the record Y has an equal chance of being X, X+1, or X+2.a) Find the joint PMF of X and Y. Y=0Y=1Y=2Y=3Y=4X=0 X=1 X=2 b) Find the conditional PMF of X given Y. Y=0Y=1Y=2Y=3Y=4X=0 X=1 X=2 c) The Y=2 column of your second table should match the marginal distribution of X. What does this say about how useful a record of "Y=2" in telling you the actual value of X?

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X given Y. Y=0 Y=1 Y=2 Y=3 Y=4 X=0 X=1 X=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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Question

A random variable X~Binomial (2, 1/3) is chosen, but the result is badly recorded; the record Y has an equal chance of being X, X+1, or X+2.

a) Find the joint PMF of X and Y.

	Y=0	Y=1	Y=2	Y=3	Y=4
X=0
X=1
X=2

b) Find the conditional PMF of X given Y.

	Y=0	Y=1	Y=2	Y=3	Y=4
X=0
X=1
X=2

c) The Y=2 column of your second table should match the marginal distribution of X. What does this say about how useful a record of "Y=2" in telling you the actual value of X?

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