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ven the joint density function below, solve for the following: 4y F(x, y) = 2x 3 + 1,0 < x < 1,0

ven the joint density function below, solve for the following: 4y F(x, y) = 2x 3 + 1,0 < x < 1,0

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Given the joint density function below, solve for the following:
F(x, y) = {2?/3 +4?/3 , 0 < ? < 1, 0 < ? < 1
                  0, elsewhere
a. Verify that f(x, y) is a joint density function. 
b. Find the P[(X, Y) ∈ A] where A ={(x,y) | /1/4 < x < 1/2 , 0 < y <  1/2}

c.Find the marginal density g(x) for the joint density function.

d. Find the marginal density h(y) for the joint density function. 
e. Find the conditional density f(y|x).
f. Find the conditional density f(x|y). 

 

Given the joint density function below, solve for the following: 2x 4y 3 ={3+* F(x, y) -, 0 < x < 1,0 <y<1 = 0, elsewhere a. Verify that f(x, y) is a joint density function. (3 points) b. Find the P[(X, Y) EA] where A = 4 {(x, y) / ²/ < x < ½ ; 0 < y <½}. (3 points) C. Find the marginal density g(x) for the joint density function. (3 points) d. Find the marginal density h(y) for the joint density function. (3 points) e. Find the conditional density f(y/x). (3 points) f. Find the conditional density f(x/y). (3 points)
Transcribed Image Text:Given the joint density function below, solve for the following: 2x 4y 3 ={3+* F(x, y) -, 0 < x < 1,0 <y<1 = 0, elsewhere a. Verify that f(x, y) is a joint density function. (3 points) b. Find the P[(X, Y) EA] where A = 4 {(x, y) / ²/ < x < ½ ; 0 < y <½}. (3 points) C. Find the marginal density g(x) for the joint density function. (3 points) d. Find the marginal density h(y) for the joint density function. (3 points) e. Find the conditional density f(y/x). (3 points) f. Find the conditional density f(x/y). (3 points)
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