solution

The following is a sufficient condition for the central limit theorem: If the random variables X1, X2, … , Xn are independent and uniformly bounded (that is, there exists a positive constant k such that the probability is zero that any one of the random variables Xi will take on a value greater than k or less than −k), then if the variance of

becomes infinite when n→q, the distribution of the standardized mean of the Xi approaches the standard normal distribution. Show that this sufficient condition holds for a sequence of independent random variables Xi having the respective probability distributions