1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Polynomial transformation of random variable

  1. Nov 19, 2011 #1
    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. jcsd
  3. Nov 20, 2011 #2
  4. Nov 20, 2011 #3
    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
     
  5. Nov 20, 2011 #4
    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 :-)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Polynomial transformation of random variable
Loading...