An estimator is said to be consistent if for any 0, as n . That is, is consistent if, as the sample size gets larger, it is less and less likely that will be further than from the true value of .

Show that is a consistent estimator of when s2 by using Chebyshev’s inequality from Exercise 44 of Chapter 3.

[Hint: The inequality can be rewritten in the form Now identify Y with .]