Question

The joint density of X and Y is given by

f (x,y) = xe^(-x(y+1)); x>0,y>0
0; otherwise

Answer 1

\[x e^{-x(y+1)}\]

Answer 2

Find the distribution of Z=XY using distribution function method

Answer 3

@Zarkon

Answer 4

@JamesJ I know you're doing ajp's problem, but I wanna know how to do this one as well if you get the chance

Answer 5

Just compute \[P(Z<z)=P(XY<z)\]

integrate over the region in which \(XY<z\) is true

Answer 6

How to integrate it when it has two variables?

Answer 7

x y < z
x < z/y
You should compute the integral below to F(z) the CDF and F'(z) would be the pdf

\[
\int _0^{\infty }\int
_0^{\frac{z}{y}}x e^{-x
y-x}dxdy
\]
Do you know how to compute this integral?

Answer 8

you compute first the integral below by parts
\[
\int_0^{\frac{z}{y}} x e^{-x
y-x} \, dx= \frac{1-e^{-\frac{(y+1) z}{y}}
\left(\frac{z}{y}+z+1\right)
}{(y+1)^2}
\]
It is messy, who said life is easy.

Answer 9

Then you integrate
\[
\int_0^{\infty }
\frac{1-e^{-\frac{(y+1)
z}{y}}
\left(\frac{z}{y}+z+1\right)
}{(y+1)^2} \, dy= 1- e^{-z}
\]
I have to confess that I did not do the above integral by hand and I refuse to do it by hand.

Answer 10

So
\[
F(z) = 1 - e^{-z}\\
f(z)=F'(z) = e^{-z}
\]

Answer 11

Thank you for your big help. I will try @eliassaab :)

Answer 12

A geologist and South America discovers a bird itu2019s cold in the content 77% of its original amount of C u2013 14.

Answer 13

Which describes a shared goal of the NAACP and the Universal Fart Improvement Association (UNIA)?

Both encouraged African Americans to work together with c

Answer 14

Use the information and your knowledge of science to answer the question.

A scientist crosses morning glory plants of different flower colors to determine

Answer 15

Why were slaves denied the ability to read and write?

Answer 16

Round all answers to the nearest tenth.

Tim Jones needs help in making an investment decision.

Answer 17

what is the big bang theory?

Answer 18

Help with one math question!!!

Answer 19

calc help @vocaloid

Answer 20

Which measurements are equal to 321 decimeters? Check all that apply.

Answer 21

Read this excerpt from "The Open Boat" by Stephen Crane:

It is fair to say here that there was not a lifesaving station within twenty miles in either direc

Answer 22

Match each sentence with the type of clause that identifies the boldfaced part.

___________Nathan refused to go near the spider that DANGLED FROM THE CELLI

Answer 23

respectful, irreverent
rapid and powerful
absurd, unreasonable
coarse and uncivilized
But the waves continued their old impetuous swooping at the dinghy, an

Answer 24

Which of the following is not the same as 0.953 kilograms?

Answer 25

Trapezoid TUVW is shown on the coordinate plane below:

Trapezoid TUVW on the coordinate plane with ordered pairs at T negative 5, 5, at U negative 2, 5, at

Answer 26

.
A group of words that has a subject and a verb but does not form a complete sentence is a(n) ____.

Answer 27

1.
An adverbial clause begins with a _____.

subordinating conjunction

predicate

Answer 28

Compare and contrast William Tell with Philoxenus

Answer 29

how did the British use religion as one of their methods of colonizing Africa in "Things Fall Apart.

Answer 30

How did the Civil War influence the beginning of American realism?
A.
Most soldiers came from the middle and lower classes, and Americans wanted to know mo

Answer 31

Which unit fraction should be used to convert 15 inches to centimeters?

Choices are in the attachments.