# Polynomial transformation of random variable

1. Nov 19, 2011

### raynard

1. The problem statement, all variables and given/known data

Given a random variable X with a known distribution (e.g. a beta distribution), find the distribution of
f(X) = X^2 + X

3. The attempt at a solution

I've tried the normal approaches: the standard transformation theorem; conditioning on X; Laplace transformation, etc. They don't seem to work. Any hints?

2. Nov 20, 2011

### Tomer

3. Nov 20, 2011

### raynard

I tried the standard method you described, but I see no easy way to find the inverse of

f: x -> x^2 + x

4. Nov 20, 2011

### Tomer

Yup, I don't think it's very pretty...
I have to say, I'm pretty rusty when it comes to probability. I remember the best ways to solve this type of questions is to write Y = X2 + X, and then:
P(Y < y) = P (X2 + X < y) = P(X2 + X - y < 0 ) = ...

Then you'd have to solve this inequality and proceed from there...
But maybe there are shortcuts. I just responded cause I saw no one else did :-)