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

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Author:Amos Gilat
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Chapter1: Starting With Matlab
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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).
Transcribed Image Text: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).
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