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:
“The real, then, is that which, sooner or later, information and reasoning would finally result in, and which is therefore independent of the vagaries of me and you. Thus, the very origin of the conception of reality shows that this conception essentially involves the notion of a COMMUNITY, without definite limits, and capable of a definite increase of knowledge.”
—Charles Sanders Peirce (1839–1914)
“... 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)
“I describe family values as responsibility towards others, increase of tolerance, compromise, support, flexibility. And essentially the things I call the silent song of life—the continuous process of mutual accommodation without which life is impossible.”
—Salvador Minuchin (20th century)
“poor Felix Randal;
How far from then forethought of, all thy more boisterous years,
When thou at the random grim forge, powerful amidst peers,
Didst fettle for the great gray drayhorse his bright and battering
sandal!”
—Gerard Manley Hopkins (1844–1889)
“The variables of quantification, ‘something,’ ‘nothing,’ ‘everything,’ range over our whole ontology, whatever it may be; and we are convicted of a particular ontological presupposition if, and only if, the alleged presuppositum has to be reckoned among the entities over which our variables range in order to render one of our affirmations true.”
—Willard Van Orman Quine (b. 1908)