ABSTRACT
Consider n independent performances of a random experiment with mutually exclusive outcomes that can be classified as success or failure.The words success and failure are to be regarded as labels for two mutually exclusive categories of outcomes of the random experiment. Yet, they may not necessarily have the ordinary connotation of success or failure. Assume that p, the probability of success on any performance of the random experiment, is constant. Let q be the probability of failure, so that
q p= 1-(5.1)
The probability distribution of X, the number of successes in n performances of the random experiment, is the binomial distribution, with a probability distribution function (pdf) specified by
f x n x n x
p q x nx n x( ) = -( )
= ¼-! ! !
