1. Suppose that the random variable Y₁, Y2, ..., Yn satisfy Yi = pi + Eis i=1,2,..., n, where x₁, x2,..., n are fixed constants, and €₁, €2, ..., En are iid N(0,0²), o² unknown. a. Find a two-dimensional sufficient statistics for (μ‚0²). b. Find the MLE of μ, and show that it is an unbiased estimator of u. Find the distribution of the MLE of µ. c. Show that Y/Σx; is an unbiased estimator of μ. d. Calculate the exact variance of Y₁/Σx, and compare it to the variance of the MLE.

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