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Math Help - Product of two independent continuous random variables

  1. #1
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    Product of two independent continuous random variables

    I have two continuous random variables X and Y. X follows an Exponential distribution with rate $\lambda$, and Y follows a Normal distribution with $\mu$ and $\sigma^2$. The domain of X is $[0,\infty)$, and that of Y is $(-\infty,\infty)$.

    I have come up with the following expression for the pdf of V=XY.
    Using the result of Rohatgi (1976, p. 141)

    f_V(v)=\frac{\lambda}{\sigma_\alpha\sqrt{2\pi}} \int_0^\infty e^{-\left(\lambda x+\frac{(\frac{v}{x}-\mu_\alpha)^2}{2\sigma_\alpha^2}\right)}\frac{1}{x  }\,dx

    Do you have any suggestions on how to solve this (analytically)?
    Last edited by basovic88; November 18th 2011 at 12:51 PM.
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  2. #2
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    Re: Product of two independent continuous random variables

    Added my Rohatgi result to the post.
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