Re: expected value ques

Posted by Amit Goyal on Jun 08, 2013; 3:27am
URL: http://discussion-forum.276.s1.nabble.com/expected-value-ques-tp7581946p7581977.html

Let M be the number of fishes in the pond before 100 tagged fishes were released. Probability of catching a tagged fish in each trial will then become 100/(100+M). Number of fishes (N) you catch till you get the tagged one is a geometric random variable with probability of success in each trial equal to 100/(100+M). Thus,
E(N) = (100+M)/100. M is estimated using P = 100 x N. For P to be an unbiased estimator of M, it must be the case that E(P) = M. Clearly,
E(P)
= 100(E(N))
= 100 + M
≠ M
Thus, the estimator P is biased.
V(P)
= 10000(V(N))
= M(100+M)