Given this joint pmf, (a) Find E(X|Y = 0). (b) Find E(YX = 1).
A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Transcribed Image Text:57. Given this joint pmf,
(a) Find E(XY = 0).
(b) Find E(YX = 1).
Transcribed Image Text:A small department has 10 faculty members of whom 3 are assistant professors (aP), 5 are associate
professors (AP), and 2 are professors (P). Of these 10 faculty members, 2 are randomly selected to be
on a committee. Let X denote the number of aP selected and let Y denote the number of AP selected.
X and Y are jointly discrete random variables with mass points (x, y) = {(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (2, 0)}.
Moreover, we can find the probability associated with each of these mass points as follows:
f(0,0)=P(X= 0, Y = 0) = P(2 P selected)
4/55
ƒ(0, 1) = P(X = 0, Y = 1) = P(1 P, 1 AP selected) = 9
=
X = Number of aP chosen
0
1
2
1/45 6/45
3/45
10/45
f(1,1)
0
10/45 0
0
(3)
=
Y = Number of AP chosen 0
1
2
⠀
= P(X = 2, Y = 0) = P(2 aP selected) ==
Leading to the joint pmf: f(x, y) = P(X = x, Y = y) =
=
H
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