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3. Let X and Y have the joint p.d.f. f(x,y)=2(x+y), 0<x<y<1. Find the marginal p.d.f. of...

3. Let X and Y have the joint p.d.f.

f(x,y)=2(x+y), 0<x<y<1.

Find the marginal p.d.f. of X and the marginal p.d.f. of Y. Determine whether Xand Y are independent.

Math   Statistics-And-Probability   
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Answer #1

The marginal PDF for X here is obtained as:

This is the required marginal PDF for X here.

The marginal PDF for Y here is obtained as:

This is the required marginal PDF for Y here.

We compute here:

which is not equal to f(x, y)

Therefore X and Y are not independent here.

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