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Math Help - Stats exam help

  1. #1
    Junior Member
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    Stats exam help

    Let Z ~ N(0,1) and
    Can anyone help with this question, have exam on saturday, each year we are asked to derive eithere the T - distribution

    T = Z/ sqr(W/r) where Z ~ N(0,1) and W ~ X2( X SQUARED) , Z and W indep


    The derivation the easy part but they ask questions on densities afterwards. Ill list a few below, Would really appreciate if anyone could help with any, test in a few hours and need a good grade to get my actuarial exemptions!

    Q1: What kindof density does T2(T squared) have?
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  2. #2
    MHF Contributor matheagle's Avatar
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    Re: Stats exam help

    F(1,r)
    and you left out the part where r is the df of the t.
    Otherwise it's a multiple of a t.

     t^2={N^2(0,1)\over \chi^2/r}={\chi_1^2/1\over \chi_r^2/r}=F(1,r)
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