MATH 1610 Lecture Notes - Lecture 18: Nan, Bernoulli Trial, Sample Space
9 Dec 2014
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Let sn be the number of successes in a binomial experiment with parameters n and p (where p is the constant probability of success on each of the n independent bernoulli trials composing the binomial experiment. Assume next that n becomes larger and larger (n goes to infinity) through more and more performances of the bernoulli trials while p remains fixed. Sn/n = x1+x2/n ie, the relative frequency of successes after n bernoulli trials, will vary in such a way that it will approach the number p with quasi-certainty. Consider any random experiment with sample space s and probability measure p. Assume this experiment can be repeated and number n of times under the same conditions. Let a be any event associated with this experiment and whose probability is p(a) let na be the random variable representing the number of times event a occurs during n repetitions.
