Suppose that the random variables Y1,..., Yn satisfy Yi = xi + i, i = 1,..., n, where x1, ..., xn are fixed constants, and

Suppose that the random variables Y1,..., Yn satisfy
Yi = βxi + ∈i, i = 1,..., n,
where x1, ..., xn are fixed constants, and ∈1,..., ∈n are iid n(0, σ2), σ2 unknown.
a. Find a two-dimensional sufficient statistic for (β, σ2).
b. Find the MLE of β, and show that it is an unbiased estimator of β.
c. Find the distribution of the MLE of β.