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

Solve x2 u2013 4 = 5 by graphing the related function.

Answer 13

Which statements describe how Antinous is portrayed in this excerpt from Book 21

Answer 14

Let g(x) = 2x and h(x) = x2 + 4.

Evaluate (h u2218 g)(u22122).

Answer 15

The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 2x2 + x u2212 3 and g(x) = x u2212 1.

Answer 16

.
The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 3x + 5 and g(x) = x2.

Answer 17

biochem question about molecules @ physiological pH (which is ~7ish)

Answer 18

Math help

Answer 19

Let g(x) = 2x and h(x) = x2 + 4.

Evaluate (h u2218 g)(1).

Answer 20

The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 3x + 5 and g(x) = x2.

Answer 21

The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 2x2 + x u2212 3 and g(x) = x + 2.

Answer 22

The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 3x + 5 and g(x) = x2.

Answer 23

Math help

Answer 24

Imagine that you are an adviser to either Chinau2019s emperor or Japanu2019s shogun.

Answer 25

a parenthetical citation for a classic play hamlet

Answer 26

analytical chem instrumentation question - main difference between a spectrofluor

Answer 27

PLEASE HELP OML!!!!!!!!!!!
1. H2 + Cl2 u2192 HCl (Need to balance equation)
How many grams of HCl can be produced if 7.

Answer 28

The youth group is going on a trip to the state fair. The trip costs $63. Included in that price is $13 for a concert ticket and the cost of 2 passes, one f

Answer 29

oh hello. :))))

Answer 30

The domain for f(x) and g(x) is the set of all real numbers.

Let f(x) = 3x + 5 and g(x) = x2.

Answer 31

Let f(x) = 2x2 + x u2212 3 and g(x) = x u2212 1.

Find f(x)/g(x) and state its do