Answered: 4y +³,0 < x < 1,0 < y <1 F(x, y) = 0,…

4y +³,0 < x < 1,0 < y <1 F(x, y) = 0, elsewhere a. Verify that f(x, y) is a joint density function. (3 points) b. Find the P[(X, Y) €A] where A = {(x, y) | 1 < x < / 0

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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Question

100%

Given thejoint densityfunction below, solve for the following:

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).

2x 4y
+¹,0 < x < 1,0 < y<1
F(x, y) = ³ 3
3
0, elsewhere
a. Verify that f(x, y) is a joint density function. (3 points)
b. Find the P[(X, Y) €A] where A = {(x, y) | ¹<x<
1/3 (
1
0<y</}.
4
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(xy).

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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