Suppose the true average growth 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 first type is s2, whereas for the second type the variance is 4s2. Let X1, . . . , Xm be m independent growth observations on the first type [so E(Xi) m, V(Xi

) s2], and let Y1, . . . , Yn be n independent growth observations on the second type [E(Yi) , V(Yi) 4s2].

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

b. For fixed m and n, compute , and then find the value of d that minimizes . [Hint: Differentiate with respect to d.]