Probability Distribution
Every random vector gives rise to a probability measure on Rn with the Borel algebra as the underlying sigma-algebra. This measure is also known as the joint probability distribution, the joint distribution, or the multivariate distribution of the random vector.
The distributions of each of the component random variables Xi are called marginal distributions. The conditional probability distribution of Xi given Xj is the probability distribution of Xi when Xj is known to be a particular value.
Read more about this topic: Multivariate Random Variable
Famous quotes containing the words probability and/or distribution:
“The source of Pyrrhonism comes from failing to distinguish between a demonstration, a proof and a probability. A demonstration supposes that the contradictory idea is impossible; a proof of fact is where all the reasons lead to belief, without there being any pretext for doubt; a probability is where the reasons for belief are stronger than those for doubting.”
—Andrew Michael Ramsay (1686–1743)
“In this distribution of functions, the scholar is the delegated intellect. In the right state, he is, Man Thinking. In the degenerate state, when the victim of society, he tends to become a mere thinker, or, still worse, the parrot of other men’s thinking.”
—Ralph Waldo Emerson (1803–1882)