Question: Question 1 (16 total points) (a) (8 points) Let X1, X2, - - , Xn be an iid random sample from a normal distribution with

I i=1 n is an unbiased estimator of 02. (b) (8 points)

Question 1 (16 total points) (a) (8 points) Let X1, X2, - - , Xn be an iid random sample from a normal distribution with parameter ,u = 0 and variance 02. Show that X? I i=1 n is an unbiased estimator of 02. (b) (8 points) If (51 and {i2 are unbiased estimator of 6, what condition must be imposed on the constants 21 and 192 so that . - 175191 + 33292 is an unbiased estimator of [9. (c) (8 points) Let X1, X2, . .. , Xn be an iid random sample from a poisson distribution with parameter A. One possible estimator for A is A given by n 1 = 1 C(X1 - Xn)2 2n Show that A is an unbiased estimator of 1

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