(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose [itex]0 < p < 1[/itex]. Define [itex]b(n,k) = \binom{n}{k}p^k(1-p)^k[/itex]. For what value of [itex]k[/itex] is [itex]b(n,k)[/itex] a maximum?

2. Relevant equations

N/A

3. The attempt at a solution

Is there any way to get a nice closed form solution to this problem? I've already proved that it has a maximum so there must be some j such that [itex]b(n,j)[/itex] is maximal. Then we know [itex]b(n,j+1) < b(n,j)[/itex] and [itex]b(n,j-1) < b(n,j)[/itex]. And I figure we can use these relations to figure out j or something like that. But I'm not sure if this approach will work.

Could someone help me with this please?

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# Homework Help: Bernoulli Trials

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