16. 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 2

, whereas for the second type, the variance is 42

. Let X1, . . . , Xm be m independent growth observations on the first type [so E(Xi

)
, V(Xi

)
2

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

)
, V(Yi

)
42

].

a. Show that for any  between 0 and 1, the estimator ˆ

X (1  )Y is unbiased for .

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