The joint probability mass function of X and Y is given by p(1, 1) = 0.05 p(2, 1) = 0.1 p(1,2) = 0.05 p(1, 3) = 0.05 p(2,2) = 0 p(2, 3) = 0.05 p(3, 1) = 0.05 p(3,2) = 0.1 p(3, 3) = 0.55 (a) Compute the conditional mass function of Y given X = 2: P(Y = 1|X = 2) = ☐ P(Y = 2X = 2) = P(Y = 3|X = 2) (b) Are X and Y independent? (enter YES or NO) (c) Compute the following probabilities: P(X + Y > 2) = P(XY = 2) = P(¥ > 1) = |
The joint probability mass function of X and Y is given by p(1, 1) = 0.05 p(2, 1) = 0.1 p(1,2) = 0.05 p(1, 3) = 0.05 p(2,2) = 0 p(2, 3) = 0.05 p(3, 1) = 0.05 p(3,2) = 0.1 p(3, 3) = 0.55 (a) Compute the conditional mass function of Y given X = 2: P(Y = 1|X = 2) = ☐ P(Y = 2X = 2) = P(Y = 3|X = 2) (b) Are X and Y independent? (enter YES or NO) (c) Compute the following probabilities: P(X + Y > 2) = P(XY = 2) = P(¥ > 1) = |
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:The joint probability mass function of X and Y is given by
p(1, 1) = 0.05
p(2, 1) = 0.1
p(1,2) = 0.05
p(1, 3) = 0.05
p(2,2) = 0
p(2, 3) = 0.05
p(3, 1) = 0.05
p(3,2) = 0.1
p(3, 3) = 0.55
(a) Compute the conditional mass function of Y given X = 2: P(Y = 1|X = 2) = ☐
P(Y = 2X = 2) =
P(Y = 3|X = 2)
(b) Are X and Y independent? (enter YES or NO)
(c) Compute the following probabilities:
P(X + Y > 2) =
P(XY = 2)
=
P(¥ > 1) = |
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