For continuous random variables X and Y with joint probability density function

Cabiolab

Cabiolab

Answered question

2021-10-19

For continuous random variables X and Y with joint probability density function
f(x,y)={xe(x+xy)x>0 and y>00otherwise
Are X and Y independent? Explain.

Answer & Explanation

comentezq

comentezq

Skilled2021-10-20Added 106 answers

The probability, P (X > 1 and Y > 1) can be calculated using the joint probability density function.
If two random variables, X and Y are independent, then the joint density function can be written as a product of the marginal density function, that is,
f(x,y)=fX(x)fY(y)
Here
f(x,y)=xe(x+xy)
fX(x)=ex
fY(y)=1(y+1)2
fX(x)fY(y)=ex(y+1)2
xe(x+xy)
f(x,y)fX(x)fY(y)
Thus, X and Y are not independent.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

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?