# Binomial distribution functions

## PDFBinomial(x,trials,probability)

PDFBinomial(x,trials,probability) returns the binomial probability of obtaining exactly x 'events' in the specified number of trials and probability of success for each trial.

Example: a fair coin is tossed 10 times. What is the probability that heads will appear exactly 5 times?

PDFBinomial(5,10,0.5) = 0.246

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## CDFBinomial(x,trials,probability)

CDFBinomial(x,trials,probability) returns the cumulative binomial probability of obtaining x or fewer 'events' in the specified number of trials and probability of success for each trial.

Example: a fair coin is tossed 10 times. What is the probability that heads will appear at most 5 times?

CDFBinomial(5,10,0.5) = 0.623

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## RNDBinomial(trials,probability)

RNDBinomial(trials,probability) generates a random number from the binomial distribution with specified number of trials and probability of success.

The mean of a random variable that has a Binomial distribution is trials x probability, and the variance is trials x probability x (1-probability).

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## BinomialLow(successes,trials,ival)

BinomialLow(successes,trials,ival) returns the lower bound of the ival% Confidence Interval of the Binomial probability of a number of successes in a number of trials

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## BinomialHigh(successes,trials,ival)

BinomialHigh(successes,trials,ival) returns the upper bound of the ival% Confidence Interval of the Binomial probability of a number of successes in a number of trials.