Let the continuous random variables X and Y have joint pdf f(x,y)=e^{-x-y}, 0

snowlovelydayM

snowlovelydayM

Answered question

2021-11-06

Let the continuous random variables X and Y have joint pdf f(x,y)=exy,0<x<,0<y<,thenf(yx)=
a)ey
b)ex
c)eyex

Answer & Explanation

jlo2niT

jlo2niT

Skilled2021-11-07Added 96 answers

Step 1
The joint pdf of the continuous random variables X and Y is given by :
f(x,y)=exy,0<x<,0<y<
Here we have to find the value of f(yx).
As we know that f(yx)=f(x,y)fX(x)
And fX(x)=abf(x,y)dy
Step 2
Let us finding the required value:
f(yx)=f(x,y)abf(x,y)dy
=exy0exydy
=exy[exy]0
=exy[eex]
=exyex
=exy+x
=ey
Thus, the required value of f(yx)=ey.
Hence, option (a) is correct.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?