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The term law of total probability is sometimes taken to mean the law of alternatives, which is a special case of the law of total probability applying to discrete random variables. [ citation needed ] One author uses the terminology of the "Rule of Average Conditional Probabilities", [ 4 ] while another refers to it as the "continuous law of ...
In combinatorics, the rule of product or multiplication principle is a basic counting principle (a.k.a. the fundamental principle of counting). Stated simply, it is the intuitive idea that if there are a ways of doing something and b ways of doing another thing, then there are a · b ways of performing both actions. [1] [2]
Bayes' theorem (alternatively Bayes' law or Bayes' rule, after Thomas Bayes) gives a mathematical rule for inverting conditional probabilities, allowing one to find the probability of a cause given its effect. [1]
A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y, the distribution of the random variable Z that is formed as the product = is a product distribution.
The measurable space and the probability measure arise from the random variables and expectations by means of well-known representation theorems of analysis. One of the important features of the algebraic approach is that apparently infinite-dimensional probability distributions are not harder to formalize than finite-dimensional ones.
The rule of sum is an intuitive principle stating that if there are a possible outcomes for an event (or ways to do something) and b possible outcomes for another event (or ways to do another thing), and the two events cannot both occur (or the two things can't both be done), then there are a + b total possible outcomes for the events (or total possible ways to do one of the things).
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