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
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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Question
Given the joint density
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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0bec7eb4-f698-4038-872f-5fbb00d8bd4c%2F208b9d3a-693d-4b22-b243-5789e59c9a56%2Fdh4hknj_processed.jpeg&w=3840&q=75)
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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