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.
Sep 16th 2013, 08:55 PM
Re: Writing PDFs
In order to find the PDF for Y = X^2 you need to use something like the transformation theorem of the characteristic equation. Do you have a particular PDF in mind? Here is the transformation theorem (scroll down to change of variables formula):
With regards to your other question, look at the definitions for expectation and marginal densities. The marginal density is used to "integrate out" the other variable so that you get a PDF in terms of one variable.
Also remember that E[XY] = Integral over region xy*f(x,y)dxdy.