5. Let f(x, y)= P(X =x,Y = y), X = 2,3,4, Y = 1,2,3, 4 , where P is given by the table below: X = 2 1/20 1/20 2/20 2/20 X = 3 X = 4 Y = 1 2/20 1/20 2/20 1/20 3/20 Y = 2 Y = 3 2/20 1/20 Y = 4 2/20 For problems (a) - (d) below write your work using the correct notation in terms of f (e.g. f(x, y), fy, fy(3), fyp: fxp(4) ): (a) Verify that f is a joint probability mass function. (b) Find the marginal distribution for each random variable. Are both random variables independent? (c) Find the mean and variance of each marginal distribution. (d) Find the conditional probability function of Y given X =3. (e) Find E(Y|X = 3) and V(Y|X = 3). (f) Find P(X+Y =5), P(Y >1), and P(X+Y = 5|Y > 1).

5. Let f(x, y)= P(X =x,Y = y), X = 2,3,4, Y = 1,2,3, 4 , where P is given by the table below: X = 2 1/20 1/20 2/20 2/20 X = 3 X = 4 Y = 1 2/20 1/20 2/20 1/20 3/20 Y = 2 Y = 3 2/20 1/20 Y = 4 2/20 For problems (a) - (d) below write your work using the correct notation in terms of f (e.g. f(x, y), fy, fy(3), fyp: fxp(4) ): (a) Verify that f is a joint probability mass function. (b) Find the marginal distribution for each random variable. Are both random variables independent? (c) Find the mean and variance of each marginal distribution. (d) Find the conditional probability function of Y given X =3. (e) Find E(Y|X = 3) and V(Y|X = 3). (f) Find P(X+Y =5), P(Y >1), and P(X+Y = 5|Y > 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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