Continuous random variable X has probability density function defined as
f(x)= 1/4 , -1<x<3
=0 , otherwise
Continuous random variable Y is defined by Y=X^2
(1) Find P(X>2) given that X>0
(2) Find G(y), the cummulative distribution function of Y
f(y)= 1/4 , 1<X<9
= 0, otherwise
Then integrate to get the cdf.
G(y)= 0 , Y<=1
= 1/4 y , 1<Y<9
=1 , Y>=9
(3) Hence find the probability density function of Y.
Then now differentiate the cdf in (2) to get the pdf
Part(2) doesn't seem right so do part(3).
My point is that if y > 1 then and so f(x) and hence the integral of f(x) is equal to 0, which means that the integration will only be non-zero for 0 < y < 1.
When y > 1, the integral is only non-zero for x > -1, that is, Case 3 is required (and I just realised that I made a typo in Case 3, the lower integral terminal shuold be -1 NOT 1. I have edited that post).
At this point, I think the best thing for you to do is print out this thread and talk it through one-on-one with your instructor.