The document presents a problem involving independent and identically distributed random variables with a given mean and variance. It asks for the variance of the sample mean, defined as the average of these random variables. The specific parameters are provided, with the task being to calculate the variance of the sample mean.

1. Problem 4 Let X i : 1 i n be independent and identically distributed random variables with mean
and variance 2 . Let X = ( n 1 ) i = 1 n X i be the sample mean. Find Var ( X ) .