Well it seemed to me like the question required exactly the same approach as the one adopted to find the cumulative distribution function F(x) ? Since you've shown me how to express P(Y<y) as P(X<y²), I simply used the same tools and broke the integral into the 3 different cases, corresponding to the different values of f(x) at different intervals. So yes it was just dumb computing but I only saw this way to operate !

I don't see mistakes in the limits of the integrals for 3) ? Or are you talking about 2) ?

This is what I thought I did with :

For y<0: F(y) = 0 so F'(y) = 0

For 0<y<1: F(y) = y² F'(y) = (1/3)

**y**^3

For 1<y : F(y) = 1 so F'(y) = 0

Is that wrong ? ahah

I might have gotten confused between Y,y and X,x and what each one represents.

Once again, thank you ! Point taken for calculus, I'm actually a law and biology student but I took a big interest math and computer science, so I'm trying to use e-learning to get a bachelor and maybe switch majors! As you can see my abilities are weak but at least I enjoy it