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Math Help - statistics_density

  1. #1
    totallystuck
    Guest

    statistics_density

    exam on Monday in this......please help!

    Let Z~N(0,1) and let W~X{r} and let Z and W be independant.

    Derive the density of the random variable

    T = Z/sqrt(W/r)



    Note: X is the chi symbol, r is a sub scribt and sqrt is square root
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  2. #2
    Newbie
    Joined
    Jan 2006
    From
    Puerto Rico
    Posts
    9

    Distribution of functions of random variables

    The standard way of proceeding in these cases is to write down the joint probability density of Z and X, integrate over the range of both subject to the condition that the function is constant with a new dummy variable.

    Since Z varies from -inf to inf and X from 0 to inf, you have to do this kind of integration. Don't give up. The question implies that there is an answer. Perhaps you can find a useful substitution.
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