Ques: If there are 'n' independent random variables i.e. X1, X2,......,Xn; each having zero mean and variance=1. If their sum is defined as Sn=X1+X2+X3+......+Xn. Then, answer the following:
(a) Find and comment on the mean and variance of (Sn/n) as n -> ∞.
(b) Find and comment on the mean and variance of (Sn/√n) as n -> ∞.
Please give the detailed explanation for the answer and also suggest some good study material on the random variables and processes.
Thanks in advance.