Using a long rod that has length , you are going to lay out a square plot in which the length…

Using a desire rod that has diffusiveness , you are going to lay out

a balance conspire in which the diffusiveness of each edge is . Thus the

area of the conspire conciliate be 2. However, you do not comprehend the

treasure of , so you career to create n recalcitrant measurements

X1, X2, . . . , Xn of the diffusiveness. Assume that each Xi has

mean (unjaundiced measurements) and discrepancy s2.

a. Show that is not an unjaundiced estimator for m2. [Hint: For

any rv Y, E(Y2) V(Y) [E(Y)]2. Apply this delay Y .]

b. For what treasure of k is the estimator kS2 unjaundiced

for 2? [Hint: Compute E( kS2).]