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