Bernoulli
We will call the Bernoulli test a random experiment with two possible outcomes, one of them is called success and the other failure with probabilities p\text{ y }1 - p = q respectively, that is:
\begin{cases} \text{P}=\{success\}=p \\ P=\{\text{failure}\} = q \\ p + q = 1 \end{cases}
The discrete v.a. \xi that takes the value 1 when in Bernoulli's experiment you get success and the value 0 if you get failure, it is said to follow a Bernoulli distribution of parameter p = P\{success\} and is denoted how to:
\xi \approx B(1, p)
Its probability function is:
P(\xi = k ) = \begin{cases} p\text{ if }k = 0 \\ q\text{ if }k = 1 \end{cases}
E(\xi) = p
\sigma^2(\xi) = p\cdot q
\sigma(\xi) = +\sqrt{p \cdot q}