- #1

Artusartos

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Since Y|X is Poisson(X), we have [itex]f(Y|X)= \frac{m^x e^{-m}}{x!}[/itex]...

Since X is [itex]Gamma(\alpha, \beta)[/itex], we have [itex]f(x)= \frac{x^{\alpha-1} e^{-x/B}}{\Gamma(\alpha) \beta^{\alpha}}[/itex]...

Since [itex]f(Y|X) = \frac{f(x,y)}{f(x)}[/itex] ====> [itex]f(x,y) = \frac{f(Y|X)}{f(x)}[/itex]...

So now we have...

[itex]f(x,y) = \frac{(\frac{m^x e^{-m}}{x!})}{\frac{x^{\alpha-1} e^{-x/B}}{\Gamma(\alpha) \beta^{\alpha}}}[/itex]

So now I have to find f(y), but I'm sort of confused...because the poisson distribution is discrete while the gamma distribution is continuous...so do I need to handle them seperately?

Thanks in advance.