7.6 Let X1, ..., Xn be independent random variables with the same distribution given by P(Xi = 0) = P(Xi = 2) = 1 4

and P(Xi = 1) = 1 2

.

Let Sn = X1 + ... + Xn.

a) Find E(Sn) and Var(Sn).

b) Give a necessary and sufficient condition on n ∈ N to have P

!1 2 ≤

Sn n

≤

3 2

"

≥ 0.999.