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# S2 Binomial distribution Q watch

1. The random variable X is distributed B(n,p). For a fixed value of n find the value of p which maximises the variance of X.

I know that I'm supposed to differentiate here, but am I correct in saying:

Var(X) = rt( np(1-p) ). Let this equal y.
dy/dp = 1/2 np(1-p)^-1/2
then...?
2. Var(X) = np(1-p). It's only a square root if you're finding standard deviation.

From there I differentiated using Var(X) = y to get dy/dp = n - 2np

To find maximum, let dy/dp = 0

So 0 = n - 2np;

n = 2np
2p = 1
so p = 0.5

Don't know if that's correct though.
3. Yes that's correct - thank you!

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Updated: October 1, 2011
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