4. The discrete random variables X and Y have known joint probability mass function с x = 0,1,2,L,9, y = 0,1,2,L,9, y≥x 0 where c = 1/55 otherwise a) Obtain the conditional PMF P(x/ Y = y) of the random variable X. b) Obtain the conditional PMFs P₂(y/X=x). c) Determine E{X/Y = 5} and var{X/Y = 5}. d) Compare the results of part c) with the same results when there is no conditioning. Py(x, y) given by Pxy(x, y) =< 3
4. The discrete random variables X and Y have known joint probability mass function с x = 0,1,2,L,9, y = 0,1,2,L,9, y≥x 0 where c = 1/55 otherwise a) Obtain the conditional PMF P(x/ Y = y) of the random variable X. b) Obtain the conditional PMFs P₂(y/X=x). c) Determine E{X/Y = 5} and var{X/Y = 5}. d) Compare the results of part c) with the same results when there is no conditioning. Py(x, y) given by Pxy(x, y) =< 3
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Transcribed Image Text:4. The discrete random variables X and Y have known joint probability mass function
P(x, y) given by Pxy(x, y) =
x = 0,1,2,L,9, y = 0,1,2,L,9, y≥x
otherwise
where c = 1/55.
a) Obtain the conditional PMF P(x/ Y = y) of the random variable X. b) Obtain the
conditional PMFs P₂(y/ X = x). c) Determine E{X / Y = 5} and var{X / Y =5}. d)
Compare the results of part c) with the same results when there is no conditioning.
3
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