Consider equation (7.33).

(a) Derive this equation using the instructions that precede it.

(b) We may often see the variance in equation (7.33) written as

Prove that the two definitions are equivalent. First, write the numerator on the right side of the equality in equation (7.33) as

Finally, divide this expression by the denominator in the term on the right side of the equality to verify that the two definitions are equivalent.

(c) Can we tell from the formula we have just derived for V(yˆ ) 0 whether ˆy0 is a consistent estimator of E(y0)? How?

V(0)=0+(-) n i=1