# Poisson distribution and expectation

(More about Poisson distributions, Part I):

Let $X$ be a random variable with Poisson $\lambda$ distribution, $\lambda> 0$ (I): Show that $E [X]k = \lambda k$ for any $k$ (- N0. (hint: $X_n= X(X-1)(X-2).........(X-k+1)$)

(II) Calculate $E = E((X-\lambda\sqrt{\lambda)})b$ for $b = 1$, $2$, $3$

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 Please use LaTEX to write your equations, and if this is homework, please add the homework tag. – Dilip Sarwate Apr 24 '12 at 18:36 Welcome to math.SE! Posting an exercise without showing you work is considered as rude. If it's a homework problem and you are looking for hints, please use the 'homework' tag. What are your thought about the problem? – Davide Giraudo Apr 24 '12 at 18:38