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Obtain the conditional density fxY=y(2).

Obtain the conditional density fxY=y(2).

A First Course in Probability (10th Edition)
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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(5) A bivariate density is x² y?, if z € (-1, 1), 0 < y < æ? f(2, y) := otherwise. The marginal densities of X and Y are 9 fx(x) = 5= x € (-1,1); fy(1) = 9y²(1 – y³/2), 0 < y < 1. Obtain the conditional density fx\y=y (x). The following answers are proposed. (a) For y € (0, 1), the conditional density of X given Y = y is 3 if y < x? < 1, fx)Y= (x) = { 2(1–g8/2) otherwise. (b) For y E (x?, 1), the conditional density of X given Y = y is 3 2(1-y3/2) if 0 < y < 1, fx}Y=y(x) = otherwise. (c) For y € (r?, 1), the conditional density of X given Y = y is if 0 < y < 1, fxyY=y (2) = { 2(1+y3/2) otherwise. .kent.edu/-kazim/login.php Home Work (d) For y e (0, 1), the conditional density of X given Y = y is 3y? if y < a? < 1, fx\Y=y(x) = { 2(1+y/2) otherwise. (e) None of the above The correct answer is (a) (b) (c) (d) (e) N/A
Transcribed Image Text:(5) A bivariate density is x² y?, if z € (-1, 1), 0 < y < æ? f(2, y) := otherwise. The marginal densities of X and Y are 9 fx(x) = 5= x € (-1,1); fy(1) = 9y²(1 – y³/2), 0 < y < 1. Obtain the conditional density fx\y=y (x). The following answers are proposed. (a) For y € (0, 1), the conditional density of X given Y = y is 3 if y < x? < 1, fx)Y= (x) = { 2(1–g8/2) otherwise. (b) For y E (x?, 1), the conditional density of X given Y = y is 3 2(1-y3/2) if 0 < y < 1, fx}Y=y(x) = otherwise. (c) For y € (r?, 1), the conditional density of X given Y = y is if 0 < y < 1, fxyY=y (2) = { 2(1+y3/2) otherwise. .kent.edu/-kazim/login.php Home Work (d) For y e (0, 1), the conditional density of X given Y = y is 3y? if y < a? < 1, fx\Y=y(x) = { 2(1+y/2) otherwise. (e) None of the above The correct answer is (a) (b) (c) (d) (e) N/A
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