I just started this topic and have a question:

For a positive continuous random variable X, write down the PDF of Y = X^2 in terms of the PDF of X.

So; writing the PDF of X, I get

P(0<X<∞) =integral from 0 to ∞ fx(x)dx

Is this correct? For Y=X^2, wouldn't the pdf be the exact same thing, since the question asks for positive continuous random variables anyway?

Is there a general method, approach I should have about this. I find pdfs to be confusing, the textbooks are heavy on jargon

And also, please see the attached image for my other question. I don't understand how to compute the integral, is there some trick?

I do believe that

to find fx(x) I integrate the joint pdf, with respect to x with the bounds set as the range of Y. But this leaves me with a very complex integration

Similarly for fy(y). Is there some trick?

Any help is greatly appreciated.