Hi People,(adsbygoogle = window.adsbygoogle || []).push({});

I have this Probability Problem which is given me a headach,

Given two independent Stochastic variables (X, Y) where X is Poisson distributed [tex]Po(\lambda)[/tex] and Y is Poisson distributed [tex]Po(\mu)[/tex].

Where [tex]\lambda[/tex], [tex]\mu > 0[/tex]. Let [tex]m \geq 0[/tex] and [tex]p = \frac{\lambda}{\lambda+ \mu}[/tex]

By the above I need to show, that

[tex]P(X=l| X+Y=m) = \left( \begin{array}{cc} l \\ m \end{array} \right ) p^l (1-p)^{(l-m)}[/tex]

Proof:

Its know that

[tex]\left( \begin{array}{cc} l \\ m \end{array} \right ) = \frac{l!}{m!(1-m)!}[/tex]

Wherefore the Binormal formula can be written as

[tex]\frac{l!}{(m!(l-m))!} p^l (1-p)^{(l-m)}[/tex]

for [tex]m \geq 0[/tex] I get:

[tex]\frac{-(\frac{\lambda + \mu}{\mu})^{l} \cdot p^{l} \cdot \mu}{l!(l!-1) \cdot (\lambda + \mu)}[/tex]

Any surgestions on how to processed from here?

Sincerely Yours

Hummingbird25

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# Homework Help: HELP: Probability Question

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