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Homework Help: 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 :-)
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