# Probability change of random variables question

## Homework Statement

I am trying to work out how to find the distribution function F$$_{Y}$$ of Y, a random variable given the distribution function F$$_{X}$$ of X and the way that Y is defined given X (see below).

Any pointers to get me started would be brilliant. I have done a similar question to this before, but can't see how to apply what I used there to this one, as previously I didn't start with F$$_{X}$$ , rather with P$$_{X}$$.

## Homework Equations

F$$_{X}$$(x) = {0 if x<1
{ $$\frac{x+1}{10}$$ if 1$$\leq$$x<$$\frac{3}{2}$$
{$$\frac{1}{3}$$(x-$$\frac{1}{2}$$ if $$\frac{3}{2}$$$$\leq$$x<$$\frac{5}{2}$$
{1 if x$$\geq$$$$\frac{5}{2}$$

and

Y = {X$$^{2}$$ if X<2
{4 if 2$$\leq$$X<3
{4(4-X) if 3$$\leq$$X<4
{0 if X$$\geq$$4

## The Attempt at a Solution

As I said, I'm not entirely sure.
Something has to be done to change it into P$$_{X}$$ I think. But I don't know how to do this.
Or should I differentiate F to get f, the density function?
But then what do I do?

Any help would be greatly appreciated.
[