5.3.7.1 __Binomial
Distribution__

The binomial distribution is used for those situations in
which there are only two outcomes, such as success or failure, and the
probability remains the same for all trials. It is very useful in
reliability and quality assurance work. The probability density function
(pdf) of the binomial distribution is

f(x) is the probability of
obtaining exactly x good items and (n-x) bad items in a sample of n items
where p is the probability of obtaining a good item (success) and q (or 1-p)
is the probability of obtaining a bad item (failure).

The cumulative distribution
function (cdf), i.e., the probability of obtaining r or fewer successes in n
trials, is given by