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.
binopdf(0,200,0.02) ans = 0.0176
What is the most likely number of defective boards the inspector will find?
defects=0:200; y = binopdf(defects,200,.02); [x,i]=max(y); defects(i) ans = 4