Challenging Estimation Question - Help needed

To show that an estimator can be consistent without being unbiased or even asymptotically unbiased, consider the following estimation procedure: to estimate the mean of a population with the finite variance s2, we first take a random sample of size *n*. Then we randomly draw one of *n* slips of paper numbered from 1 through *n*, and if the number we draw is 2,3,…, or *n*, we use as our estimator the mean of the random sample; otherwise, we use the estimate *n*2. Show that this estimation procedure is

a) consistent;

b) neither unbiased nor asymptotically unbiased.

Find the variance of this estimator.