Using the fact that for any random variables X1, X2, …, Xn and any numbers a1, a2, …, an,...

Using the fact that for any random variables X₁, X₂, …, X_n and any numbers a₁, a₂, …, a_n, show that if X₁, X₂, …, X_n are IID random variables with mean μ and variance σ², then and E[S²(n)] = σ². Show that the first result still holds if the X_i’s are dependent.