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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- July 5th 2008, 04:37 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) - July 5th 2008, 06:42 AMmr fantastic
- July 5th 2008, 06:56 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 - July 5th 2008, 01:58 PMCaptainBlack
- July 5th 2008, 09:29 PMyoavperelThank you all , it's very helpfull ..
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- September 28th 2009, 10:00 PMyvonnehrx^2 question
- October 1st 2009, 10:09 AMMoo
- July 26th 2010, 03:48 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)