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$\ (X_1,X_2,X_3,X_4)$ has a multinomial distribution with parameters $\frac{3\theta}5, \frac{\theta}5,\frac{\theta}5,1-\theta$ Calculate the fisher information where $\theta$ is in $[0,1]$.

So I wrote out the likelihood function, took the log of it and differentiated wrt $\theta$. I got

$\frac{x_1+x_2+x_3}\theta - \frac{x_4}{1-\theta}$. how do I work out the expectation of this?

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    differentiate twice, or take second moment of what you have, but 1) that doesn't look right (because $x_1$ should have different coefficient that $x_2,x_3$) and 2) is a linear function of the $x_i$, so is easy to take the expectation of.2012-06-07
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    You might compute the expectations $E(x_i)$ and plus these into your formula.2012-06-13

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