Can anyone provide a proof for the variance of poisson distribution?

Show that it is Var(N(t)) = lamda*t without using the Bernoulli distribution and independence way..( which is the typical way of summations or expectations)

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- Jul 5th 2008, 03:37 AMyoavperelneed help variance of poisson dist.
Can anyone provide a proof for the variance of poisson distribution?

Show that it is Var(N(t)) = lamda*t without using the Bernoulli distribution and independence way..( which is the typical way of summations or expectations) - Jul 5th 2008, 05:42 AMmr fantastic
- Jul 5th 2008, 05:56 AMMoo
There is another way I've learnt, using generating function (not sure you know it...)

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Now, we know that

and

Linearity of mean :

Therefore - Jul 5th 2008, 12:58 PMCaptainBlack
- Jul 5th 2008, 08:29 PMyoavperelThank you all , it's very helpfull ..
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- Sep 28th 2009, 09:00 PMyvonnehrx^2 question
- Oct 1st 2009, 09:09 AMMoo
- Jul 26th 2010, 02:48 AMundine99To Mr. Fantastic
Thanks a lot, i hv been thinking of this proof in other methods and cannot figure it out until i found this simple one.(Clapping)