Binomial Distribution — Cumulative Probabilities

Table 5. Binomial Distribution—Cumulative Probabilities P (continued)...

The cumulative binomial distribution is given by equation 2.5-33, where M is the number of f ailures out of items each having a probability of failure p. This can be worked backH tirLh lo find tlic implied value of p for a specified P(M, p,... 

By extension, the probability that a given number of actives or fewer should occur in a given distribution is described by the cumulative binomial distribution function, calculated as... 

Table 5. Binomial Distribution. This is a discrete distribution representing the probabilities of success in N trials for a population or sample in which only two outcomes are possible, but for which the eventual outcome is fixed and known if an infinite number of trials are made.f This eventual outcome is fixed by the conditions, such as 0.5 for one face of a coin or 0.1667 for one face of a six-sided die. Values in the body of the table represent the cumulative piobabihty of X or more successes in N trials. In applications to acceptance or attribute sampling, the table gives the probability of X or more acceptances (or rejections) in a single sample of N items. In either case the known or fixed probability of the result (success or failure) for the entire population is represented by p.

The optional MATLAB statistics toolkit contains several functions for evaluating the binomial distribution, binornd generates random munbers according to the binomial distribution, binofit fits a bmomial distribution to a data set, binostat computes the mean and variance, binopdf returns the probability distribution, and the cumulative distribution and its inverse are returned by binocdf and binoinv. Similar routines are available for a host of other coimnon probabihty distributions (see the toolkit documentation for a list). 

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