y2 41 ГО.1 0.157P(X, Y) = x3 0.20.3%3D5 Lo.1 0.15]a) Evaluate the marginal distribution of X and Y.b) Find P(Y/X) and P(X/Y).c) Find P(Y=2/X=3).

Answered: y 2 4 1 ГО.1 0.157 P(X, Y) = x3 0.2 0.3…

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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y
2 4
1 ГО.1 0.157
P(X, Y) = x3 0.2
0.3
%3D
5 Lo.1 0.15]
a) Evaluate the marginal distribution of X and Y.
b) Find P(Y/X) and P(X/Y).
c) Find P(Y=2/X=3).

Expert Solution

Step 1

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Step 2

The joint and marginal probability mass function of X and Y is as follows:

From the joint probability table, the marginal probability mass functions are as follows:

Step 3

The condition probability P(Y|X) is calculated as follows:

The P(Y|X) is obtained by dividing each joint probability by corresponding row total.

That is,

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