1. X_1,..., X_n ~ iid ~N(0,1). Define X bar (sample mean) and S^2=sum_1^n(X^2_i).
a) Show that X bar and S^2 are dependent.
b) Derive the conditional distribution of X bar, given S^2.
c) Determine c(u) such that P[X bar c(u)|u] =alpha, where u = S^2.