Compute the binomial distribution. Consider an uncertain event where there are two outcomes only, typically success or failure. Flipping a coin is an example: The outcome is uncertain and of two...

Compute the binomial distribution.

Consider an uncertain event where there are two outcomes only, typically success or failure. Flipping a coin is an example: The outcome is uncertain and of two types, either head (can be considered as success) or tail (failure). Throwing a die can be another example, if (e.g.) getting a six is considered success and all other outcomes represent failure. Let the probability of success be p and that of failure 1−p. If we perform n experiments, where the outcome of each experiment does not depend on the outcome of previous experiments, the probability of getting success x times (and failure n − x times) is given by

This formula (4.8) is called the binomial distribution. The expression x! is the factorial of x as defined in Exercise 3.14. Implement (4.8) in a function binomial(x, n, p). Make a module containing this binomial function. Include a test block at the end of the module file. Name of program file: binomial_distribution.py.