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
Chapter6: Exponential And Logarithmic Functions
Section6.7: Exponential And Logarithmic Models
Problem 27SE: Prove that bx=exln(b) for positive b1 .
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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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