16. Suppose the true average growth m of one type of plant during a 1-year period is identical to that of a second type, but the variance of growth for the rst type is s2, whereas for the second type, the variance is 4s2. Let X1, . . . , Xm be m independent growth observations on the rst type [soE(Xi)m,V(Xi)s2], and let Y1, . . . , Yn be n independent growth observations on the second type [E(Yi)  m, V(Yi)  4s2].

a. Show that for any constant d between 0 and 1, the estimator is unbiased for m.

b. For xed m and n, compute V( ), and then nd the value of d that minimizes V( ). [Hint: Differentiate V with respect to d.]