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please help Suppose we have two independent samples (X1,X2, ,Xn) and (Y1, Y2, - -- ,Ym) from two different normal distributions: Assume that of and

please help
Suppose we have two independent samples (X1,X2, ,Xn) and (Y1, Y2, - -- ,Ym) from two different normal distributions: Assume that of and 0% are known. Now we would like to do some inference on #1 + 2pm. In this case, a natural approach is to study X + 217, which is a consistent and unbiased estimator of [41 + 2pm. (a) (4pt) Find the distribution of X + 217. (b) (5pt) Find a (nontrivial) (1 or) condence interval for #1 | 2,112. (c) (5pt) Suggest a test statistic and construct a level or test for H0 : p1 +2,u.g = 0 vs H1 : p1 +2p2 % 0

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