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We collect a random sample (also known as independent and identically distributed sample (ID))X1, X2.... Xn from a population, where E(Xi)=andVar(Xi)=02. We then form

 

We collect a random sample (also known as independent and identically distributed sample (ID))X1, X2.... Xn from a population, where E(Xi)=andVar(Xi)=02. We then form Xn, which is a sample average. What is true about the sample average? 1. It is just a constant; not a random variable. 2. It is a random variable with E(Xn) = un. 3. It is a random variable with E(Xn) = . 4. The sample average Xn is a biased estimator of u. 5. If the sample is random, the sample average Xn is not a consistent estimator of u.

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