Assume that X1, X2, ..., Xn are independent random variables with possibly different
distributions and let Sn be their sum. Let mk = E(Xk), \sigma 2
k = V AR(Xk), and Mn =
m1 + m2 + · · · + mn. Assume that \sigma 2
k < R and mk < T for all k. Prove that, for any
\epsi > 0,
P (| Sn
n − Mn
n | < \epsi ) -> 1
as n -> \infty using Chebyshev’s inequality.