# pdfBinomial¶

## Purpose¶

Computes the binomial probability density function.

## Format¶

p = pdfBinomial(successes, trials, prob)
Parameters:
• successes (NxK matrix, Nx1 vector or scalar) – must be a positive number and < trials

• trials (NxK matrix, Nx1 vector or scalar) – ExE conformable with successes. trials must be > successes.

• prob (NxK matrix, Nx1 vector or scalar) – The probability of success on any given trial. ExE conformable with successes. $$0 < prob < 1$$.

Returns:

p (NxK matrix, Nx1 vector or scalar) – The probability of the specified number of successes.

## Examples¶

A polling company randomly selects 1,024 prospective voters in a region where 55% support their candidate. What is the probability that exactly 600 of those selected support their candidate?

p = pdfBinomial(600, 1024, 0.55);


After running the code above, p is equal to:

0.0017226334


Continuing with the example above, what would be the probability of selecting the same number of voters that support their candidate if their candidate’s support in the region was 50% or 60%?

p_support = { 0.5, 0.6 };
p = pdfBinomial(600, 1024, p_support);


After running the code above, p is equal to:

6.3351627e-09
0.016621105


## Remarks¶

The probability density function for the binomial distribution is defined as:

$$P\left( x = k \middle| n,p \right) =$$ $$\begin{pmatrix} n \\ k \\ \end{pmatrix}p^{k}\left( 1 - p \right)^{n - k}$$

where k is the number of successes, n is the number of trials and p is the probability of success on each trial.

For invalid inputs, pdfBinomial() will return a scalar error code which, when its value is assessed by function scalerr(), corresponds to the invalid input. If the first input is out of range, scalerr() will return a 1; if the second is out of range, scalerr() will return a 2; etc.