Let X1Xn be a random sample of size n from the exponential d

Solution

A point estimator ˆ is said to be an unbiased estimator of , if E[theta] =
, for every possible value of . If ˆ is not unbiased, the difference E[ˆtheta] is called the
bias of .
Proposition 1.1 When X is a Binomial r.v. with parameters n, p, the sample proportion
ˆp = X/n is an unbiased estimator of p.

f X1,X2, . . . ,Xn is a random sample from a distribution with mean ,
1 then ¯X is an unbiased estimator of .
2 If in addition the distribution is continuous and symmetric, then any trimmed mean
is also unbiased estimators of .
3 If the distribution has a variance, 2. Then the estimator
ˆ2 = S2 =
P
(Xi ¯X)2
n 1
is an unbiased estimator of 2.