# Probability distribution

Probability distribution is a term from mathematics. Suppose there are many events with random outcomes. A probability distribution is the theoretical counterpart to the frequency distribution. A frequency distribution simply shows how many times a certain event occurred. A probability distribution says how many times it should have occurred in the long run (that is, its probability). The probability distribution of a random variable ${\displaystyle X}$ is often written as ${\displaystyle f_{X}(x)}$ (or simply ${\displaystyle f(x)}$).[1][2] Such a distribution can either be discrete, taking a discrete (or countable) amount of values, or continuous, taking an uncountable amount of values (as from a continuous interval).[3]

As an example, the probability distribution for a single roll of a normal 6-sided dice can be presented by:

 Result Probability of result ${\displaystyle 1}$ ${\displaystyle 2}$ ${\displaystyle 3}$ ${\displaystyle 4}$ ${\displaystyle 5}$ ${\displaystyle 6}$ ${\displaystyle {\frac {1}{6}}}$ ${\displaystyle {\frac {1}{6}}}$ ${\displaystyle {\frac {1}{6}}}$ ${\displaystyle {\frac {1}{6}}}$ ${\displaystyle {\frac {1}{6}}}$ ${\displaystyle {\frac {1}{6}}}$

where result is the outcome of the dice roll, and the probability shows the chances of that result occurring. If we roll a dice 60 times, then in the long run, we should expect to have each side appear 10 times on average.

There are different probability distributions.[4] Each of them has its use, its benefits and its drawbacks. Some common probability distributions include:

## References

1. "List of Probability and Statistics Symbols". Math Vault. 2020-04-26. Retrieved 2020-09-11.
2. Bourne, Murray. "11. Probability Distributions - Concepts". www.intmath.com. Retrieved 2020-09-11.
3. "1.3.6.1. What is a Probability Distribution". www.itl.nist.gov. Retrieved 2020-09-11.
4. "Normal Distribution - easily explained! | Data Basecamp". 2021-11-26. Retrieved 2023-05-29.