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Math Help - finding a distribution

  1. #1
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    Post finding a distribution

    Given a random sample from population with density function f(x; ) = √() exp[-πx]

    Prove that 2πx is distributed as X(1) ( chi square with 1 degree of freedom).

    How would I approach this using moments generating function?
    [Originally is meant to be a symbol for lamda)
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  2. #2
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    Re: finding a distribution

    So \phi is a constant determining the distribution and x is the random variable?
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  3. #3
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    Re: finding a distribution

    is the parameter . Like how lamda is the parameter for the poisson or how mu and sigma are parameters of the normal distribution.
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  4. #4
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    Re: finding a distribution

    I am pretty sure that a Chi squared random variable is equal to a normally distributed random variable squared.
    Show that x is normally distributed then show that 2πx has one degree of freedom
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  5. #5
    MHF Contributor matheagle's Avatar
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    Re: finding a distribution

    Just compare this to the chi-square density in your book.
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