Polynomial transformation of random variable

  • Thread starter raynard
  • Start date
  • #1
9
0

Homework Statement



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

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?
 

Answers and Replies

  • #3
9
0
Thanks for the reply!

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

f: x -> x^2 + x
 
  • #4
202
0
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 :-)
 

Related Threads on Polynomial transformation of random variable

  • Last Post
Replies
3
Views
2K
Replies
2
Views
1K
  • Last Post
Replies
3
Views
1K
Replies
6
Views
1K
Replies
11
Views
2K
Replies
2
Views
3K
Replies
7
Views
2K
Replies
1
Views
1K
Top