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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# HELP: Probability Question

**Physics Forums | Science Articles, Homework Help, Discussion**