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## Homework Statement

I am trying to work out how to find the distribution function F[tex]_{Y}[/tex] of Y, a random variable given the distribution function F[tex]_{X}[/tex] 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[tex]_{X}[/tex] , rather with P[tex]_{X}[/tex].

## Homework Equations

F[tex]_{X}[/tex](x) = {0 if x<1

{ [tex]\frac{x+1}{10}[/tex] if 1[tex]\leq[/tex]x<[tex]\frac{3}{2}[/tex]

{[tex]\frac{1}{3}[/tex](x-[tex]\frac{1}{2}[/tex] if [tex]\frac{3}{2}[/tex][tex]\leq[/tex]x<[tex]\frac{5}{2}[/tex]

{1 if x[tex]\geq[/tex][tex]\frac{5}{2}[/tex]

and

Y = {X[tex]^{2}[/tex] if X<2

{4 if 2[tex]\leq[/tex]X<3

{4(4-X) if 3[tex]\leq[/tex]X<4

{0 if X[tex]\geq[/tex]4

## The Attempt at a Solution

As I said, I'm not entirely sure.

Something has to be done to change it into P[tex]_{X}[/tex] 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.

Many thanks in advance.

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