(New page: So where <math>\hat n_{ML} = \text{max}_n ( \binom{n}{1000000} p^{1000000} (1-p)^{n-1000000} )</math> we can express x! as a gamma function but the derivative is kind of a mess. If yo...) |
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we can express x! as a gamma function but the derivative is kind of a mess. If you were to take the derivative of the the rest of the function you would find | we can express x! as a gamma function but the derivative is kind of a mess. If you were to take the derivative of the the rest of the function you would find | ||
| − | <math> {1000000}p^{999999} * -{n-1000000} *(1-p)^{n-1000001} </math> = 0 | + | <math> {1000000}p^{999999} * -{(n-1000000)} *(1-p)^{n-1000001} </math> = 0 |
Revision as of 18:16, 10 November 2008
So where
$ \hat n_{ML} = \text{max}_n ( \binom{n}{1000000} p^{1000000} (1-p)^{n-1000000} ) $
we can express x! as a gamma function but the derivative is kind of a mess. If you were to take the derivative of the the rest of the function you would find
$ {1000000}p^{999999} * -{(n-1000000)} *(1-p)^{n-1000001} $ = 0
