Independence (statistics)
Probability theory talks about events which occur with a given (possibly unknown) probability. Sometimes, when it talks about several events occurring, it assumes that if one event occurs, this does not change the probability of the other events occurring.
More specifically, two events [math]\displaystyle{ A }[/math] and [math]\displaystyle{ B }[/math] are called independent (written as [math]\displaystyle{ A \,\bot\, B }[/math][1]), if the probability of [math]\displaystyle{ A }[/math] occurring is the same whether [math]\displaystyle{ B }[/math] is assumed to have occurred or not.[2] Alternatively, [math]\displaystyle{ A }[/math] and [math]\displaystyle{ B }[/math] are independent precisely when the probability of them occurring together is equal to the product of their individual probabilities.[3]
Abraham de Moivre wrote:[4] "Two events are independent, when they have no connexion one with the other, and that the happening of one neither forwards nor obstructs the happening of the other."
Independence (statistics) Media
Pairwise independent, but not mutually independent, events
Mutually independent events
Related pages
References
- ↑ "Compendium of Mathematical Symbols". Math Vault. 2020-03-01. Retrieved 2020-09-21.
- ↑ "Probability - Independent events | Brilliant Math & Science Wiki". brilliant.org. Retrieved 2020-09-21.
- ↑ Weisstein, Eric W. "Independent Events". mathworld.wolfram.com. Retrieved 2020-09-21.
- ↑ Abraham de Moivre (1718). "The Doctrine of Chance".