Suppose $X\sim binomial (n,0.5)$ and set $Y=log(X)$ (base 2 is better, but any base would do). How do I compute the expectation of $Y$, or find a good lower bound?
Thanks.
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There is a problem with your question. The standard support (alphabet) of a binomial distribution is $k\in {0,1,\ldots,n}$. But for $k=0$, $Y$ takes an infinite value. Could you spell out in full the binomial distribution as you intend it? – Pierpaolo Vivo Mar 02 '16 at 13:54
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You are right. I need to define $Y=log(X+\alpha)$, and this is already answered in Mathoverflow http://mathoverflow.net/questions/145678/expected-value-of-logarithm-of-a-binomial-random-variable . – mike Mar 02 '16 at 15:52