$\ (X_1,X_2,X_3,X_4)$ 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?