If the expected value of the sample statistic is equal to the population parameter being estimated, the sample statistic is said to a. have low variability. b. be an unbiased estimator of the population parameter. c. have high precision. d.be a random estimator of the population parameter.

The definition of unbiased estimator states that if the population parameter which is to be estimated is equal to the expected value of sample statistic then the estimator will be an unbiased estimator.

For example consider the sample statistic x bar and population parameter μ the xbar is an unbiased estimator of μ i.e. E(xbar)=μ

We can show that E(xbar)=μ in the following steps

Now expected value of sample statistic= E(xbar)

As we know that xbar= sumxi/n where i ranges from 1 to n. So,

E(Xbar)=E(sumxi/n)

n is constant so,

E(Xbar)=(1/n)E(sumxi)

where sumxi= x1+x2+...+xn.

E(xbar)=(1/n)(E(x1)+E(x2)+...+E(xn))

E(xbar)=(1/n)(μ+μ+...+μ)

E(xbar)=(1/n)(nμ)

E(xbar)=μ

Hence xbar is an unbiased estimator of population parameter μ.

So, if the expected value of the sample statistic is equal to the population parameter being estimated, the sample statistic is said to be an unbiased estimator of the population parameter