The independent random variables $\displaystyle Y_{1},Y_{2},...,Y_{n},$ each $\displaystyle Y_{i}\in\{0,1\}$, are postulated to depend on covariates $\displaystyle x_{1},x_{2},...,x_{n}$ through the model,
$\displaystyle log\frac{\pi_{i}}{1-\pi_{i}}=\beta x_{i}$

a) Derive the equation which the maximum likelihood estimator of $\displaystyle \beta$ satisfies.

b) For the special case where each $\displaystyle x_{i} \in \{-1,0,1\}$ solve the equation in part (a). You may assume that the number of $\displaystyle x_{i} = j$ is $\displaystyle n_{j}$, $\displaystyle j=-1,0,1$ and that $\displaystyle y_{i}=1$ for $\displaystyle r_{j}$ of the cases where $\displaystyle x_{i}=j$


I'm really stuck on the part (b), can anyone either point me in the right direction or come up with a solution? Thanks!