(a) Consider the IID sequence {Xk, k N} with E(Xk) = 0, Var(Xk) = 2. Define...

(a) Consider the IID sequence {Xk, k ∈ N} with E(Xk) = 0, Var(Xk) = σ2. Define the sequence {Yk, k ∈ N}, where Yk = a + bXk, k = 1, 2, . . . Do the SLLN, WLLN, and CLT hold for the sequence {Yk, k ∈ N}? Explain your answer.

(b) Consider the stochastic process {Xk, k ∈ N} that satisfies E(Xk) = 0, Var(Xk) = σ2, and Cov(Xi, Xj) = c|i−j|, for 0

Does the WLLN hold for the sequence {Xk, k ∈ N}? Explain your answer.