Independent Identically Distributed Continuous Random Variables
For n independent and identically distributed continuous random variables X1, X2, ..., Xn with cumulative distribution function G(x) and probability density function g(x) the range of the Xi is the range of a sample of size n from a population with distribution function G(x).
Read more about this topic: Range (statistics)
Famous quotes containing the words independent, identically, distributed, continuous, random and/or variables:
“It is so rare to meet with a man outdoors who cherishes a worthy thought in his mind, which is independent of the labor of his hands. Behind every man’s busy-ness there should be a level of undisturbed serenity and industry, as within the reef encircling a coral isle there is always an expanse of still water, where the depositions are going on which will finally raise it above the surface.”
—Henry David Thoreau (1817–1862)
“... two men could be just alike in all their dispositions to verbal behavior under all possible sensory stimulations, and yet the meanings or ideas expressed in their identically triggered and identically sounding utterances could diverge radically, for the two men, in a wide range of cases.”
—Willard Van Orman Quine (b. 1908)
“Indiana was really, I suppose, a Democratic State. It has always been put down in the book as a state that might be carried by a close and careful and perfect organization and a great deal of—[from audience: “soap”Ma reference to purchased votes, the word being followed by laughter].
I see reporters here, and therefore I will simply say that everybody showed a great deal of interest in the occasion, and distributed tracts and political documents all through the country.”
—Chester A. Arthur (1829–1886)
“Perhaps when distant people on other planets pick up some wave-length of ours all they hear is a continuous scream.”
—Iris Murdoch (b. 1919)
“And catch the gleaming of a random light,
That tells me that the ship I seek is passing, passing.”
—Paul Laurence Dunbar (1872–1906)
“Science is feasible when the variables are few and can be enumerated; when their combinations are distinct and clear. We are tending toward the condition of science and aspiring to do it. The artist works out his own formulas; the interest of science lies in the art of making science.”
—Paul Valéry (1871–1945)