A random $0$-$1$ event (say, flipping a coin) is said to follow a Bernoulli distribution with probability $p$ if the probability of a $1$ is $p$ and the probability of a $0$ is $1 - p$ where $0 \le p \le 1$.

A fair coin would follow a Bernoulli distribution with $p = \frac{1}{2}$.

Implement a function that returns a $1$ with probability $p$.

Use an assertion to ensure that the argument $p$ falls in the desired interval.

The rand(), found in the cstdlib library, returns an integer between 0 and RAND_MAX, inclusive.

Now, be careful, for if $p = 0$, then this function should always return a $0$ and if $p = 1$, then this function should always return a $1$.

#include <cstdlib>
#include <cassert>

// Function declaration
int bernoulli( double p );

Class implementation

Implement a class Bernoulli_distribution where:

• The constructor Bernoulli_distribution::Bernoulli_distribution( double p ); takes an argument $p$ and creates an instance that generates random values that follow the Bernoulli distribution.
• The member function int Bernoulli_distribution::operator()() const; returns a $1$ with probability $p$ and $0$ with probability $1 - p$.