7.14 Under the assumptions of Problem 7.13, if B = b1 +···+bN is known, an alternative unbiased estimator a¯ is



1 n

n i=1 Yi Zi b¯ + n(N − 1)

(n − 1)N



Y¯ −



1 n

n i=1 Yi Zi Z¯



.

[Hint: Use the facts that E(Y1/Z1) = (1/N)(ai/bi) and that by the preceding problem E

 1 n − 1



Yi Zi

(Zi − Z¯)



=

 1 N − 1

 ai bi

(bi − b¯)



.]