(a) Show that T=aT1 + (1 – a) T2 is also an unbiased estimator of 0 for any constant a. (b) Find the value of a which minimizes the variance of T.

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Chapter1: Combinatorial Analysis
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1. Suppose T1 and T2 are independent unbiased estimators of a parameter 0, with variances
of and o, respectively.
(a) Show that T= aT1 + (1- a) T2 is also an unbiased estimator of 0 for any constant a.
(b) Find the value of a which minimizes the variance of T.
Transcribed Image Text:1. Suppose T1 and T2 are independent unbiased estimators of a parameter 0, with variances of and o, respectively. (a) Show that T= aT1 + (1- a) T2 is also an unbiased estimator of 0 for any constant a. (b) Find the value of a which minimizes the variance of T.
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