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Math Help - Probability Integral Transformation Question

  1. #1
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    Probability Integral Transformation Question

    Hello,

    I have the following problem presented to me. How would you go about solving this?

    Suppose that Y has a c.d.f. given by:

    F(y) = 1 - 9/(y^2), for y>=3
    0 otherwise

    a.) Find a transformation G(U) so that G(U) has a c.d.f. F when U has a uniform distribution on the interval (0,1).
    b.) Given that a random sample of size 3 from a uniform distribution on the interval (0,1) yielded the values 0.0058, 0.2048, and 0.7692, use the transformation derived in part (a) to give values associated with a random variable with the same distribution as Y.


    How would you go about solving this? Thanks for any help. I greatly appreciate it.
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  2. #2
    MHF Contributor
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    Re: Probability Integral Transformation Question

    Hey piazzaj.

    To start you off I would have a look at the following result:r

    Inverse transform sampling - Wikipedia, the free encyclopedia

    (Look at how the inverse cumulative function of any random variable is related to the U[0,1] distribution).
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