Let X1, X2, ..., Xn be a random sample from a population with mean mu and varian

Question

Let X1, X2, ..., Xn be a random sample from a population with mean mu and variance Sigma ^2 LT Infinity . Recall that in PSTAT 120B, this is equivalent to writing X1, X2, ... , Xn (mu, Sigma ^2), where Sigma ^2 LT Infinity . Note that we haven't told you a specific family of distributions - you are only told that the random variables are iid, each with mean mu and variance Sigma ^2. Let x = and s^2 = X is known as the sample mean, and S^2 is known as the sample variance. You may assume any basic expectation and variance rules that you proved in PSTAT 120A, such as E(cXi) = cE(Xi) if c is a constant. Find the following expected values, clearly showing your working. Your answers may depend on the unknown parameters mu and Sigma ^2. E(X) Var (X) E [S^2]

Explanation / Answer

Let X1, X2, ..., Xn be a random sample from a population with mean mu and varian

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