The probability function

The probability function is the random variable $X$ that associates a probability $p_{i}$ to every possible value of $X$ $(x_{1}, x_{2}, \dots, x_{n})$ . We also need: $\begin{matrix} 0 \leq p_{i} \leq 1 \\ p_{1} + p_{2} + p_{3} + \dots + p_{n} = \sum_{i} p_{i} = 1 \end{matrix}$

Example

Let the random variable $X$ be the result of throwing a dice. Supposing that it has six equiprobable faces, the probabilities of every result are: $p (X = 1) = P (X = 2) = \dots = P (X = 6) = \frac{1}{6}$ It is possible to prove that we have $\sum_{i} p_{i} = 6 \cdot \frac{1}{6} = 1$ The graph of the above mentioned function is a bar chart:

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