Suppose that the random variables Y1,..., Yn satisfy Yi = xi + i, i = 1,..., n,

Question:

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 of the MLE of β.
Distribution
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