In: Statistics and Probability
Let X1, X2, · · · , Xn (n ≥ 30) be i.i.d observations from N(µ1, σ12 ) and Y1, Y2, · · · , Yn be i.i.d observations from N(µ2, σ22 ). Also assume that X's and Y's are independent. Suppose that µ1, µ2, σ12 , σ22 are unknown. Find an approximate 95% confidence interval for µ1µ2.