Illustration Of The Central Limit Theorem
This article gives two concrete illustrations of the central limit theorem. Both involve the sum of independent and identically-distributed random variables and show how the probability distribution of the sum approaches the normal distribution as the number of terms in the sum increases.
The first illustration involves a continuous probability distribution, for which the random variables have a probability density function.
The second illustration, for which most of the computation can be done by hand, involves a discrete probability distribution, which is characterized by a probability mass function.
A free full-featured interactive simulation that allows the user to set up various distributions and adjust the sampling parameters is available through the External links section at the bottom of this page.
Read more about Illustration Of The Central Limit Theorem: Illustration of The Continuous Case, Illustration of The Discrete Case
Famous quotes containing the words illustration of, illustration, central, limit and/or theorem:
“What is character but the determination of incident? What is incident but the illustration of character?”
—Henry James (1843–1916)
“Each truth that a writer acquires is a lantern, which he turns full on what facts and thoughts lay already in his mind, and behold, all the mats and rubbish which had littered his garret become precious. Every trivial fact in his private biography becomes an illustration of this new principle, revisits the day, and delights all men by its piquancy and new charm.”
—Ralph Waldo Emerson (1803–1882)
“There has never been in history another such culture as the Western civilization M a culture which has practiced the belief that the physical and social environment of man is subject to rational manipulation and that history is subject to the will and action of man; whereas central to the traditional cultures of the rivals of Western civilization, those of Africa and Asia, is a belief that it is environment that dominates man.”
—Ishmael Reed (b. 1938)
“Moreover, the universe as a whole is infinite, for whatever is limited has an outermost edge to limit it, and such an edge is defined by something beyond. Since the universe has no edge, it has no limit; and since it lacks a limit, it is infinite and unbounded. Moreover, the universe is infinite both in the number of its atoms and in the extent of its void.”
—Epicurus (c. 341–271 B.C.)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)