Joint Probability: Definition, History, and Further Reading
Joint probability is a statistical concept that describes the probability of two or more events occurring simultaneously. It is a measure of the likelihood of the intersection of two or more events. It is also known as “joint probability distribution” or “joint probability density”. Joint probability is used to calculate the probability of any combination of two or more events.
The concept of joint probability has been used in mathematics since ancient times. The earliest known mention of the concept can be found in the writings of Aristotle in 350 BC. He states, “For when one thing is said to be probable with reference to or in conjunction with another, the probability of each is not the same as if it were considered separately; but the probability of the conjunction is a compound of the two.” This idea was further explored by other mathematicians and philosophers, including Blaise Pascal and Pierre de Fermat in the 17th century.
In the 19th century, the concept of joint probability was further developed by Pierre-Simon Laplace and Augustin-Louis Cauchy. Laplace developed the concept of “joint probability distribution,” which is now widely used in statistical analysis. Cauchy developed the concept of “joint probability density” to describe the probability of two or more events occurring simultaneously.
Today, joint probability is a fundamental concept in probability theory and statistics. It is used to calculate the probability of any combination of two or more events occurring together. It is also used to calculate the probability of an event occurring given the occurrence of one or more other events.
Further Reading
Aristotle. (350 BC). Topics. Translated by E.S. Forster. Cambridge, MA: Harvard University Press.
Laplace, P.S. (1812). Théorie Analytique des Probabilités. Paris: Courcier.
Cauchy, A.L. (1825). Résumé des leçons données à l’École Royale Polytechnique sur le calcul des probabilités. Paris: Bachelier.
Feller, W. (1968). An Introduction to Probability Theory and Its Applications. New York: John Wiley and Sons.
Kotz, S., & Johnson, N.L. (1969). Continuous Multivariate Distributions. New York: John Wiley and Sons.