Suppose U and V1,...,Vn are IID N (0, 1) variables; is a real number. Let Xi

Suppose U and V1,...,Vn are IID N (0, 1) variables; µ is a real number. Let Xi = µ + U + Vi. Let X = n−1 n i=1 Xi and s2 =

(n − 1)−1 n i=1(Xi − X)2.

(a) What is the distribution of Xi?

(b) Do the Xi have a common distribution?

(c) Are the Xi independent?

(d) What is the distribution of X? of s2?

(e) Is there about a 68% chance that |X − µ| < s/√n?