Range (statistics) - Independent Identically Distributed Continuous Random Variables

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:

    Men will say that in supporting their wives, in furnishing them with houses and food and clothes, they are giving the women as much money as they could ever hope to earn by any other profession. I grant it; but between the independent wage-earner and the one who is given his keep for his services is the difference between the free-born and the chattel.
    Elizabeth M. Gilmer (1861–1951)

    they were placed in a box
    and painted identically blue
    and thus passed their days
    living happily ever after
    a kind of coffin,
    a kind of blue funk.
    Anne Sexton (1928–1974)

    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)

    For good and evil, man is a free creative spirit. This produces the very queer world we live in, a world in continuous creation and therefore continuous change and insecurity.
    Joyce Cary (1888–1957)

    We should stop looking to law to provide the final answer.... Law cannot save us from ourselves.... We have to go out and try to accomplish our goals and resolve disagreements by doing what we think is right. That energy and resourcefulness, not millions of legal cubicles, is what was great about America. Let judgment and personal conviction be important again.
    Philip K. Howard, U.S. lawyer. The Death of Common Sense: How Law Is Suffocating America, pp. 186-87, Random House (1994)

    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)