..Alright, in this one, I'm given X~U(-1, 3) -1<x<3
Y = X²
Ok, so I know that the domain of y should be 0 < y< 9...right? Mr F says:Yes.
Oh, and the pdf(x) = 1/4, -1 < x< 3 Mr F says: Yes.
So I said, F(y) = P(Y <= y) = P(X² <= y) = P(X <= (y)^1/2
Mr F says: I think this is what you should have:
Now do the integrations to get the cdf F(y) and then differentiate to get the pdf f(y).
My question is...how do I know the domain for this f(y). Is it for the whole 0<y<9? Or just part? If just part of it, how do I get the other f(y).
Mr F says: Note that there are three parts to the rule:
1. f(y) = 0 for values of y less than 0 or greater than 9.
2. f(y) = ...... when .
3. f(y) = ...... when .
Next question is how do I find the Cox(X,Y) over a continuous function? I know how to get marginal and mean, but not covariance.
Mr F says: Cov(X, Y) = E(XY) - E(X) E(Y).
You get E(X) and E(Y) in the usual way.
To get E(XY) you need to find the joint distribution f(x,y) of X and Y (unless theres some easy way specific to the actual problem. See http://www.mathhelpforum.com/math-he...oach-time.html for example). Then , with appropriate integral terminals of course.