(Solved):
Let XBin(n,p), where the probability of success p is unknown and is estimated, as usual, by p^ ...
Let X∼Bin(n,p), where the probability of success p is unknown and is estimated, as usual, by p^=nX. Show that the statistic T=n−1n2p^(1−p^) is an unbiased estimator of σX2
To show that T = 2(1-p) is an unprejudiced assessor of p, we want to compute the normal worth of T and contrast it with the genuine worth of p.
We realize that the normal worth of T is given by:
E(T) = E(2(1-p)) = 2E(1-p) = 2(1 - E(p))
where E(p) is the genuine worth of the obscure bo...