**6. Binomial distribution**

It is one of the discrete distributions in which the experiment can be repeated for (n) times so that the probability of success is (p) and the probability of failure is (1-p), so that the probability density function has the following formula [13]:

$$\mathbf{f}(\mathbf{x}) = \binom{\mathbf{n}}{\mathbf{x}} \mathbf{p}^{\mathbf{x}} (\mathbf{1} - \mathbf{p})^{\mathbf{n}-\mathbf{x}}, \mathbf{x} = \mathbf{0}, \mathbf{1}, \dots, \mathbf{n} \tag{40}$$

and the average is:

$$\mathbf{E}(\mathbf{x}) = \mathbf{n}\mathbf{p} \tag{41}$$

The variance is:

$$
\sigma^2 = \text{np}(\mathbf{1} - \mathbf{p}) \tag{42}
$$
