In this problem we develop a weak law of large numbers for

Question

In this problem, we develop a weak law of large numbers for a correlated sequence X₁, X₂,... of identical random variables. In particular, each X_i has expected value E[X_i] = µ, and the random sequence has covariance function

Where a is a constant such that |a|

(a) Use Theorem 6.2 to show that

(b) Use the Chebyshev inequality to show that for any c > 0,

(c) Use part (b) to show that for any c > 0,