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Suppose there are two correlated random variables $X_1$ and $X_2$ both are gamma distributed but having different shape and scale parameters with correlation coefficient $\rho$. What will be the distribution of Y? where $Y=(2X_1 X_2)/(X_1+X_2)$.

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    $\begingroup$ You say these variables are correlated. So the distribution of $Y$ will depend on the joint distribution of $X_1$ and $X_2$ (which knowing their individual distributions is insufficient to determine). $\endgroup$
    – Robin Chapman
    Commented Aug 18, 2010 at 6:47
  • $\begingroup$ @Robin Chapman, To find solution of this question, if more information required, i am providing link for joint distribution of $X_1$ and $X_2$. onlinelibrary.wiley.com/doi/10.1002/hyp.259/pdf $\endgroup$
    – user8576
    Commented Aug 18, 2010 at 8:37
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    $\begingroup$ @dikuve: Instead of referring the reader to a non freely accessible paper, you might want to address Robin's remark that the joint distribution of $(X_1,X_2)$ being not entirely determined by 1. the probability distribution of $X$, 2. the probability distribution of $Y$ and 3. the correlation coefficient $\rho$, your question has no answer (or, if these three parameters are enough to determine the probability distribution of $Y$, to explain why this is so). $\endgroup$
    – Did
    Commented Jan 9, 2011 at 17:40

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