Regression through the origin: $\hat\alpha=\sum x_iz_i/\sum z_i^2$

Let $X_1,X_2,\dots,X_n$ be iid r.v.s satisfying the regression equation $X_i=\alpha z_i+e_i$; $i=1,\dots,n$, where $z_1,\dots,z_n$ are fixed and the $e_i$'s are iid $N(0,\sigma^2)$, $\sigma^2$ unknown. The MLE of $\alpha$ is given as: