Poisson distribution

**acevipa** · June 4th 2010, 04:42 AM

Let X be a discrete random variable with Poisson distribution with parameter $\lambda$

1) Show that:

$E(X^2)=\sum_{k=1}^{\infty} \frac{ke^{-\lambda} \lambda^k}{(k-1)!}$

2) By changing the summation variable, show that $E(X^2)=\lambda E(X)+\lambda$

3) Using (2), show that $Var(X)=\lambda$

**mr fantastic** · June 4th 2010, 06:31 AM

Originally Posted by acevipa

Let X be a discrete random variable with Poisson distribution with parameter $\lambda$

1) Show that:

$E(X^2)=\sum_{k=1}^{\infty} \frac{ke^{-\lambda} \lambda^k}{(k-1)!}$

2) By changing the summation variable, show that $E(X^2)=\lambda E(X)+\lambda$

3) Using (2), show that $Var(X)=\lambda$

Read this thread: http://www.mathhelpforum.com/math-he...sson-dist.html

**acevipa** · June 4th 2010, 06:56 AM

Originally Posted by mr fantastic

Read this thread: http://www.mathhelpforum.com/math-he...sson-dist.html

Thanks so much. That answered my question completely.

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