2. (20 pts) Let the joint p.m.f. of X and Y be defined by f(x, y) = 3x + y 45 x = 1, 2, 3 y = 1,2 a) Find P(X - Y ≥ 1) b) Find the marginal pmf of Y. c) Find the conditional pmf of X given Y = 1. d) Find E(X|Y = 1).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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2. (20 pts) Let the joint p.m.f. of X and Y be defined by
f(x, y) =
3x+y
45
x = 1, 2, 3 y = 1,2
a) Find P(X-Y≥ 1)
b) Find the marginal pmf of Y.
c) Find the conditional pmf of X given Y = 1.
d) Find E(X|Y = 1).
Transcribed Image Text:2. (20 pts) Let the joint p.m.f. of X and Y be defined by f(x, y) = 3x+y 45 x = 1, 2, 3 y = 1,2 a) Find P(X-Y≥ 1) b) Find the marginal pmf of Y. c) Find the conditional pmf of X given Y = 1. d) Find E(X|Y = 1).
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