An estimator ^ is said to be consistent if for any e > 0, P(|^ - | e) ( as ( `. That

An estimator θ^ is said to be consistent if for any e > 0, P(|θ^ - θ| ≥ e) ( ∞ as ( θ`. That is, θ^ is consistent if, as the sample size gets larger, it is less and less likely that θ^ will be further than e from the true value of θ. Show that  is a consistent estimator of m when σ2 < ∞ by using Chebyshev's inequality from Exercise 44 of Chapter 3.