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 class of citizens who provide at once their own food and their own raiment, may be viewed as the most truly independent and happy.”
—James Madison (17511836)
“Here I sit down to form characters. One I intend to be all goodness; All goodness he is. Another I intend to be all gravity; All gravity he is. Another Lady Gish; All Lady Gish she is. I am all the while absorbed in the character. It is not fair to sayI, identically I, am anywhere, while I keep within the character.”
—Samuel Richardson (16891761)
“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: soapMa 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 (18291886)
“The gap between ideals and actualities, between dreams and achievements, the gap that can spur strong men to increased exertions, but can break the spirit of othersthis gap is the most conspicuous, continuous land mark in American history. It is conspicuous and continuous not because Americans achieve little, but because they dream grandly. The gap is a standing reproach to Americans; but it marks them off as a special and singularly admirable community among the worlds peoples.”
—George F. Will (b. 1941)
“Man always made, and still makes, grotesque blunders in selecting and measuring forces, taken at random from the heap, but he never made a mistake in the value he set on the whole, which he symbolized as unity and worshipped as God. To this day, his attitude towards it has never changed, though science can no longer give to force a name.”
—Henry Brooks Adams (18381918)
“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 (18711945)