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 o, whereas for the second type the variance is  402.

Let X,.... X be m independent growth observations on the first type [so E(X) =, V(X)=], and let Y,..., Y, be n independ- ent growth observations on the second type [E(Y) = , V(Y) = 40].

a. Show that for any 8 between 0 and 1, the estimator =8x+(18) is unbiased for .

b. For fixed m and n, compute V(), and then find the value of 8 that minimizes V(). [Hint: Differentiate () with respect to 8.]