Exercise Solution 4.3
- We first prove the technical result. This involves no random quantities. It is just algebra:
- We next use our technical result to determine the bias of the sample variance estimator
The derivation is
To obtain the next step in the derivation, we apply the result of Exercise 3.15 twice:
We conclude that sample estimator [4.5] is biased.
- Finally, we determine the bias of the alternative estimator of variance
which we can denote
The derivation largely parallels that of part (b):
Estimator [4.27] is unbiased.