hello

if x~bi(n;x,θ) then for which θ the probability is the max?

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- Apr 19th 2010, 09:25 PM #1

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- Apr 19th 2010, 10:37 PM #2

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- Apr 19th 2010, 11:58 PM #3

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- Apr 20th 2010, 01:04 AM #4

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You have a RV $\displaystyle N \sim B(x,\theta)$

Now you ask for what value of $\displaystyle \theta$ is:

$\displaystyle b(n;x,\theta)=\frac{n!}{x!(n-x)!} \theta^n (1-\theta)^{n-1}$

maximised.

Start by observing the required $\displaystyle \theta$ is a solution of:

$\displaystyle \frac{\partial}{\partial \theta}b(n;x,\theta)=0$

CB