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Binomial Distribution
Concept of the binomial distribution, binomial PDF and CDF, expectation and variance of binomial distribution
Concept of the binomial distribution, binomial PDF and CDF, expectation and variance of binomial distribution
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The binomial distribution models situations where the same action is repeated multiple times, each with the same chance of success. It has two key numbers: the number of attempts (​n​) and the probability of success in each attempt (​p​).
If a random variable ​X​ follows a binomial distribution, we write ​X∼B(n,p).
The binomial probability density function (aka pdf) is a function that models the likelihood of obtaining ​k​ successes from ​n​ trials where the likelihood of success of each trial is ​p. We calculate the probability of exactly ​k​ successes in ​n​ trials, ​P(X=k), using the calculator's binompdf function.
Press 2nd ​→​ distr ​→​ binompdf(. Once in the binompdf function, write your ​n​ value after "trials," your ​p​ value after "p," and your ​k​ value after "x value." Then hit enter twice and the calculator will return the probability you are interested in.
The distr button is located above vars . Once in the distr menu, you can also click alpha ​→​ A to navigate to the binompdf function.
The binomial cumulative density function tells us the probability of obtaining ​k​ or fewer successes in ​n​ trials, each with a likelihood of success of ​p. We calculate the probability of less than or equal to ​k​ successes in ​n​ trials, ​P(X≤k), using the calculator's binomcdf function.
Press 2nd ​→​ distr ​→​ binomcdf(. Once in the binomcdf function, write your ​n​ value after "trials," your ​p​ value after "p," and your ​k​ value after "x value." Then hit enter twice and the calculator will return the probability you are interested in.
The distr button is located above vars . Once in the distr menu, you can also click alpha ​→​ B to navigate to the binomcdf function.
If ​X∼B(n,p), then
and