Suppose that {y1, y2, y3} denote a random sample from an exponential distribution with density function f(y) = 1 ? e ?y/?, for y > 0 0 otherwise. Consider the following five estimators: ??1 = y1, ??2 = y1 + y2 2 , ??3 = y1 + 2y2 3 , ??4 = min {y1, y2, y3} , ??5 = Y

(a) Which of these estimators are unbiased?

(b) Among the unbiased estimators, which has the smallest variance

Suppose that {311,242,313} denote a random sample from an exponential distribution with density function () 69/9, for y > 0 0 otherwise. f(y)={ Consider the following ve estimators: A A + A +2 A . A 6123/1: 62=y1 2y2: 632%: 64=m1n{y1,y2,y3}, 65=Y (a) Which of these estimators are unbiased? (b) Among the unbiased estimators, which has the smallest variance