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Binomial probability density function


Y = binopdf(X,N,P)


Y = binopdf(X,N,P) computes the binomial pdf at each of the values in X using the corresponding number of trials in N and probability of success for each trial in P. Y, N, and P can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions of the other inputs.

The parameters in N must be positive integers, and the values in P must lie on the interval [0, 1].

The binomial probability density function for a given value x and given pair of parameters n and p is


where q = 1 – p. The result, y, is the probability of observing x successes in n independent trials, where the probability of success in any given trial is p. The indicator function I(0,1,...,n)(x) ensures that x only adopts values of 0, 1, ..., n.


A Quality Assurance inspector tests 200 circuit boards a day. If 2% of the boards have defects, what is the probability that the inspector will find no defective boards on any given day?

ans =

What is the most likely number of defective boards the inspector will find?

y = binopdf(defects,200,.02);
ans =

Introduced before R2006a

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