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1. The problem statement, all variables and given/known data

I am trying to prove that the poisson distribution is normalized, I think I've got an ok start but just having trouble with the next step.

2. Relevant equations

A counting experiment where the probability of observing n events (0≤n<∞) is given by:

P(n) = (μ^n)/n! * e^(-μ)

Where μ is a real number.

3. The attempt at a solution

Background(possibly incorrect)

So it's discrete, as n will take integer values; I need a sum not an integral.

Ʃ P(n) from n=0 to ∞ is just given by:

Ʃ (μ^n)/n! * e^(-μ)

And e^(-μ) does not vary with n, so:

Ʃ P(n) = e^(-μ) * Ʃ (μ^n)/n!

Important bit

Now as I am trying to prove it is normalized, i need to get Ʃ P(n) = 1, so I assume my problem is getting from:

(μ^n) / n!

to

e^μ

Any tips or help would be much appreciated, thanks in advance.

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# Homework Help: Proving the poisson distribution is normalized

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