1Blurb:: 2Aleatory uncertain discrete variable - binomial 3Description:: 4The binomial distribution describes probabilities associated with a series 5of independent Bernoulli trials. 6A Bernoulli trial is an event with two mutually exclusive outcomes, 7such as 0 or 1, yes or no, success or fail. 8The probability of success remains the same (the trials are independent). 9 10The density function for the binomial distribution is given by: 11\f[f(x) = \left(\begin{array}{c}n\\x\end{array}\right){p^x}{(1-p)^{(n-x)}}\f] 12where \c p is the 13probability of failure per trial, \c n is the number of trials and 14\c x is the number of successes. 15 16Topics:: discrete_variables, aleatory_uncertain_variables 17Examples:: 18Theory:: 19The binomial distribution is typically used to predict the number of failures 20or defective items in a total of \c n independent tests or trials, 21where each trial has the probability \c p of failing or being defective. 22 23Faq:: 24See_Also:: 25