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The joint probability mass function of X and Y is given by p(1,1) = 0.05 p(1,2) = 0.1 p(2, 1) = 0.1 p(3, 1) = 0.05 p(1,3) = 0.05 p(2, 2) = 0.25 p(2,3) = 0.1 p(3, 2) = 0.1 p(3,3) = 0.2 (a) Compute the conditional mass function of Y given X = 2: P(Y = 1|X = 2) = Р(Y — 2|X — 2) — %3D P(Y = 3|X = 2) = || (b) Are X and Y independent? (enter YES or NO) NO (c) Compute the following probabilities: P(X+Y > 3) = Р(XҮ — 3) —D P(주 > 2) =

The joint probability mass function of X and Y is given by p(1,1) = 0.05 p(1,2) = 0.1 p(2, 1) = 0.1 p(3, 1) = 0.05 p(1,3) = 0.05 p(2, 2) = 0.25 p(2,3) = 0.1 p(3, 2) = 0.1 p(3,3) = 0.2 (a) Compute the conditional mass function of Y given X = 2: P(Y = 1|X = 2) = Р(Y — 2|X — 2) — %3D P(Y = 3|X = 2) = || (b) Are X and Y independent? (enter YES or NO) NO (c) Compute the following probabilities: P(X+Y > 3) = Р(XҮ — 3) —D P(주 > 2) =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The joint probability mass function of X and Y is given by p(1, 1) = 0.05 p(1,2) = 0.1 p(2, 1) = 0.1 p(3, 1) = 0.05 p(3,2) = 0.1 p(1,3) = 0.05 p(2, 2) = 0.25 p(2,3) = 0.1 p(3, 3) = 0.2 (a) Compute the conditional mass function of Y given X = 2: P(Y = 1|X = 2) = P(Y = 2|X = 2) = P(Y = 3|X = 2) =|| (b) Are X and Y independent? (enter YES or NO) NO (c) Compute the following probabilities: Р(Х + Y > 3) %3 Р(XҮ — 3) — P(\ > 2) =
Transcribed Image Text:The joint probability mass function of X and Y is given by p(1, 1) = 0.05 p(1,2) = 0.1 p(2, 1) = 0.1 p(3, 1) = 0.05 p(3,2) = 0.1 p(1,3) = 0.05 p(2, 2) = 0.25 p(2,3) = 0.1 p(3, 3) = 0.2 (a) Compute the conditional mass function of Y given X = 2: P(Y = 1|X = 2) = P(Y = 2|X = 2) = P(Y = 3|X = 2) =|| (b) Are X and Y independent? (enter YES or NO) NO (c) Compute the following probabilities: Р(Х + Y > 3) %3 Р(XҮ — 3) — P(\ > 2) =
Expert Solution
Step 1

Joint probability distribution: is defined as two discrete random variables which are functioning at time "t"

with the range of these random variables

 

Formula:

The formula  for the conditional probability of Y=y and given X=x is as follows:

P(Y=y|X=x)=P(Y=y|X=x)P(X=x)

P(X>x, Y>y)=∑x,yP(x,y)

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