# Math Help - Functions of Random Variables

1. ## Functions of Random Variables

Suppose that the pdf of a random variable X is as follows:
f(x)= 1/2 x for 0<x<2
0 otherwise

Also, suppose that Y=X(2-X). Determine the df and the pdf of Y.

I am new to this and very clueless and the book is not helping at all, if anyone could help explain how to start this problem to me. Thank you

Suppose that the pdf of a random variable X is as follows:
f(x)= 1/2 x for 0<x<2
0 otherwise

Also, suppose that Y=X(2-X). Determine the df and the pdf of Y.

I am new to this and very clueless and the book is not helping at all, if anyone could help explain how to start this problem to me. Thank you
Start by calculating the cdf: $F(y) = \Pr(Y < y) =Pr(2X - X^2 < y)$ and note that the support of Y is $0 \leq y \leq 1$. Drawing a diagram will help.

The pdf is dF/dy.

3. I am confused on finding F(y). I integrate f(x)dx but over what? 0 to 1?