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:

    We are independent of the change we detect. The longer the lever, the less perceptible its motion. It is the slowest pulsation which is the most vital. The hero then will know how to wait, as well as to make haste. All good abides with him who waiteth wisely; we shall sooner overtake the dawn by remaining here than by hurrying over the hills of the west.
    Henry David Thoreau (1817–1862)

    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 say—I, identically I, am anywhere, while I keep within the character.
    Samuel Richardson (1689–1761)

    Taking food alone tends to make one hard and coarse. Those accustomed to it must lead a Spartan life if they are not to go downhill. Hermits have observed, if for only this reason, a frugal diet. For it is only in company that eating is done justice; food must be divided and distributed if it is to be well received.
    Walter Benjamin (1892–1940)

    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)

    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)