Counting & Binomial Distribution

Counting

$n$ is any non-negative integer and $0 \leq k \leq n$

This method takes under consideration the combination of a number with itself as well.

Let $X$ be the random variable counting the number of hits in a Bernoulli scheme at $n$ repetitions.

The law of $X$ is the binomial law of parameters $n$ and $p$ and we have:

Where $n$ is any non-negative integer and $0 \leq k \leq n$

.