Consider a sequence X1, X2, ..., Xn of independent and identically distributed random variables with mean m and variance . The sample mean of this sequence is defined by
The weak law of large numbers states
is called the relative frequency or empirical frequency of the event A. Let p = [A] denote the probability of the event A.
The experiment is said to exhibit "statistical regularity" if the relative frequency Mn is most likely to be within e of p for large n. Use the weak law of large numbers, considered in Problem, to justify this statement.