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Math Help - Help with probability density function questions

  1. #1
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    Help with probability density function questions

    Let {N(t):t>=0} be a poisson process of rate 1 and let T1 < T2 <... denote the times of the points. Derive the pdf of Y=T1/T3 and obtain E(Y).

    Let X,Y be iid N(0,1). Derive the pdf of W=|x|/Y.

    Could someone please help me with this kind of pdf questions?

    Thanks a lot!
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  2. #2
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    Re: Help with probability density function questions

    The times T1, T2, ..., Tn are sums of exponentials and have Gamma distributions (see here). The ratio between two Gamma is a compound Gamma (see here)
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  3. #3
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    Re: Help with probability density function questions

    Thanks for the reply, so both T1 and T3 have gamma distributions? I don't really know how to derive a compound gamma equations, can you explain a little bit more?
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    Re: Help with probability density function questions

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