# Hypergeometric distribution - How do I evaluate this expected value?

Suppose to have a random variable $X$ which follows an hypergeometric distribution (see this as reference).

Let $P(X = k) = p_k$ and $g(X, K) = \max(0, aX + b(K+1))$.

I would like to evaluate the expected value of $g(X, K)$:

$$\mathbb{E}[g(X, K)] = \sum_k g(k,K)p_k$$

Some suggestion?

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What makes you think the obvious summation can be simplified? –  Did Feb 2 '13 at 13:03
I hope that it can be simplified and for this reason I asked it here :D –  the_candyman Feb 2 '13 at 13:13
"Abandon all hope, ye who enter here"... :-) –  Did Feb 2 '13 at 17:53
Ok. So, for general pdf and general $g(X)$, are there some techniques to obtain upper and lower bound for $\mathbb{E}[g(X)]$? –  the_candyman Feb 3 '13 at 13:04
My previous comment answers this. –  Did Feb 4 '13 at 12:38