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, 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 (if it doesn't, check your answer). What does this say about how useful a record of "Y=2" in telling you the actual value of X?

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, 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 (if it doesn't, check your answer). What does this say about how useful a record of "Y=2" in telling you the actual value of X?

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

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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, 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 (if it doesn't, check your answer). What does this say about how useful a record of "Y=2" in telling you the actual value of X?

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