Suppose we have samples of size n and m for two different normal populations. X1, X2, . . . , Xn ∼ N(µx, σ2 x ) Y1, Y2, . . . , Ym ∼ N(µy, σ2 y ) where µx, µy are unknown, but variances σ 2 x , σ2 y are known.

(a) (2pts) Construct a point estimator for the difference in means, i. e. µx − µy.