I have two random variables [tex]X[/tex] and [tex]Y[/tex]. Now the distribution of [tex]X[/tex] and [tex]Y[/tex], is a bit complicated. Basically they follow Gamma distributions, [tex]X=\Gamma(k1,\theta)[/tex] and [tex]Y=\Gamma(k2,\theta)[/tex], but [tex]k1[/tex] and [tex]k2[/tex] are Poisson distributed. But I do have a closed form expression for the distribution of [tex]X[/tex] and [tex]Y[/tex], and also have an expression for their mean and variances.(adsbygoogle = window.adsbygoogle || []).push({});

Now what I would like to do is find an expression for the mean and variance of [tex]X/(X+Y)[/tex].

So I'd like to know, is there a short way of getting the mean and variance of [tex]X/(X+Y)[/tex], from the mean and variance of [tex]X[/tex] and [tex]Y[/tex] and if not, then how would I go about finding the mean and variance of [tex]X/(X+Y)[/tex].

Any ideas??

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# Functions of random variables

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