9. Two discrete random variables X and Y have joint probability mass function (pmf) 1,2,...,n; y = 1, 2, . . . , x. f(x) = { k n(n+1) 0 Xx = otherwise (d) Use the fact that E(Y) = Ex (Ey\x(Y|X)), where Ex( ) and Ey|x( ) are the expected values with respect to X and with respect to Y given X, respectively, to show that E(Y) = n(n+³) 4
9. Two discrete random variables X and Y have joint probability mass function (pmf) 1,2,...,n; y = 1, 2, . . . , x. f(x) = { k n(n+1) 0 Xx = otherwise (d) Use the fact that E(Y) = Ex (Ey\x(Y|X)), where Ex( ) and Ey|x( ) are the expected values with respect to X and with respect to Y given X, respectively, to show that E(Y) = n(n+³) 4
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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Transcribed Image Text:9.
Two discrete random variables X and Y have joint probability mass function
(pmf)
1,2,...,n; y = 1, 2, . . . , x.
f(x) = {
k
n(n+1)
0
Xx =
otherwise
(d)
Use the fact that E(Y) = Ex (Ey\x(Y|X)), where Ex( ) and Ey|x( ) are the
expected values with respect to X and with respect to Y given X, respectively,
to show that E(Y) = n(n+³)
4
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