 # 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

## Calculator

 PDFBinomial( ,, )

## Graph Function: PDFBinomial(,,) X-axis Y-axis Minimum: Maximum: ## 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

## Calculator

 CDFBinomial( ,, )

## Graph Function: CDFBinomial(,,) X-axis Y-axis Minimum: Maximum: ## 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).

## Calculator

 RNDBinomial( , )

## 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

## Calculator

 BinomialLow( ,, )

## 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.

## Calculator

 BinomialHigh( ,, )