Problem 1. Suppose that the random variables $Y_1, \dots, Y_n$ satisfy
$Y_i = \beta x_i + \epsilon_i$, for $i = 1, \dots, n;$
where $x_1, \dots, x_n$ are fixed known constants, $\beta$ is a fixed unknown parameter to be esti-
mated, and $\epsilon_1, \dots, \epsilon_n \stackrel{iid}{\sim} N(0, \sigma^2)$, with $\sigma^2$ unknown.
(a) Find the MLE of $\beta$.
(b) Find the MLE of $\sigma^2$.