Answer:
Let X1,X2,...,Xn be i.i.d. random variables with expected value EXi=μ<∞ and variance 0<Var(Xi)=σ2<∞. Then, the random variable
Zn=X¯¯¯¯−μσ/n−−√=X1+X2+...+Xn−nμn−−√σ
converges in distribution to the standard normal random variable as n goes to infinity, that is
limn→∞P(Zn≤x)=Φ(x), for all x∈R,
where Φ(x) is the standard normal CDF.
Step-by-step explanation:
