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Help Finding new PDFs in Terms of a given one

  1. Feb 21, 2005 #1

    I put together the following by trying to make sense of my notes. I discussed this with a classmate and we had some disagreement, so I would like to know if I'm doing it correctly.

    Assume that X is normally distributed with mean mu m and variance sigma s squared.

    So Based on the above assumption, this implies X's pdf is:

    (1/(sqrt(2 pi) s))*exp((-1/2)((x-m)/s)^2)

    So far okay?

    Ok so now the problem is: Find the PDF of Y = X^2.

    I have a relationship P(X <= t) = integral( f(x), x, -inf, t) where f(x) is the pdf of x.

    So I do, P(Y <= t) = P( -sqrt(t) <= X <= sqrt(t)) = ugly integral.

    Then I differentiate using the Fundamental Theorem of Calculus to get rid of the integral, and that result is my PDF for X^2. The work is pretty messy so I won't post it, and I'm confident I did that part correctly. I'm just wondering if the process outlined above is correct.
    Last edited: Feb 21, 2005
  2. jcsd
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