1. Let X1, X2, X, be a random sample from a population having mean u and...

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1. Let X1, X2, X, be a random sample from a population having mean u and variance .... o2. Consider the following estimators of u. X1 + 2X2 + X3 X1 + 2X2 — Xз + 4 02 4 a) (2 pts) Calculate E[0,]. b) (2 pts) Calculate E[02]. c) (2 pts) Calculate Var[0,]. d) (2 pts) Calculate Var[02]. e) (2 pts) Discuss the properties of the 0, and 02. Which estimator is better? Explain. 1. Let X1, X2, X, be a random sample from a population having mean u and variance .... o2. Consider the following estimators of u. X1 + 2X2 + X3 X1 + 2X2 — Xз + 4 02 4 a) (2 pts) Calculate E[0,]. b) (2 pts) Calculate E[02]. c) (2 pts) Calculate Var[0,]. d) (2 pts) Calculate Var[02]. e) (2 pts) Discuss the properties of the 0, and 02. Which estimator is better? Explain.