1. Consider a random variable W with unknown population mean y. We have four estimators for 4. They are ſi, ji and it. T

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1 Consider A Random Variable W With Unknown Population Mean Y We Have Four Estimators For 4 They Are Si Ji And It T 1 (47.44 KiB) Viewed 33 times

1. Consider a random variable W with unknown population mean y. We have four estimators for 4. They are ſi, ji and it. The estimators have the following distributions: N(21, ơ), 7 N1, 2ơ), 1 x N(II, vº), 1 x NV, 0.lơ). where o > 2 . For î, the above distribution of N(244, 04) indicates that E() = 2 and Var(fi) = o?: the other estimators' mean and variance are defined in the same fashion. (a) (10 points) Is there an unbiased estimator of in the above? Find all unbiased estimators and explain what it means for an estimator to be unbiased. (b) (10 points) Find the most efficient estimator out of the four estimators. You must explain for full credit. (c) (10 points) Suppose we want to pick one estimator between ji and it. It is known that and o = 3, which estimator would you choose using the menti squared error criterion? Show your work. 2. (5 points) Let Z be the standard normn random variables that is, Z-N(0.1). What is the value of P(-1.5 20.12)