***3. State and prove Baye's theorem. (May-05, Mar-09,12
hamulccion
Answers
Step-by-step explanation:
In probability theory and statistics, Bayes’s theorem (alternatively Bayes’s law or Bayes’s rule) describes the probability of an event, based on prior knowledge of conditions that might be related to the event[1]. For example, if the probability that someone has cancer is related to their age, using Bayes’ theorem the age can be used to more accurately assess the probability of cancer than can be done without knowledge of the age.
One of the many applications of Bayes’ theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in Bayes’ theorem may have different probability interpretations. With Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to Bayesian statistics.
Bayes’ theorem is named after Reverend Thomas Bayes (/beɪz/; 1701?–1761), who first used conditional probability to provide an algorithm (his Proposition 9) that uses evidence to calculate limits on an unknown parameter, published as An Essay towards solving a Problem in the Doctrine of Chances (1763). In what he called a scholium, Bayes extended his algorithm to any unknown prior cause. Independently of Bayes, Pierre-Simon Laplace in 1774, and later in his 1812 Théorie analytique des probabilités, used conditional probability to formulate the relation of an updated posterior probability from a prior probability, given evidence. Sir Harold Jeffreys put Bayes's algorithm and Laplace’s formulation on an axiomatic basis. Jeffreys wrote that Bayes’ theorem “is to the theory of probability what the Pythagorean theorem is to geometry.”[2]