Homework 6

Problem 1: Prove: A sequence of rv's Xn converges to a constant c in distribution, then it also converges to c in probability.

Problem 2 Say we have a sequence of iid rv's X1, X2, .. and assume that E[Xi]=m and Var[Xi]=s2 exist. Define

The first and the last are called the sample mean and the sample standard deviation (of the first n of these). Show