Let T1 and T2 be two independent unbiased estimators of some parameter 6, and furthermore suppose that a? = m(Tl) 75 03 = var(T2) - Suppose that the two estimators are combined by means of a weighted average to give the estimator T=aT1+(1o:)T2 , where a is a constant such that 0 5 a 5 1. 1. Show that T is also an unbiased estimator of 9. 2. Find the value of Cr (as a function of of and 03) that minimises var(T). 3. Under what conditions (in terms of of and 0.3,) is it better to use (T1 + T2)/2 than either T1 or T2 alone to estimate 9