Probability Density Function - Products and Quotients of Independent Random Variables

Products and Quotients of Independent Random Variables

See also: Product distribution and Ratio distribution

Given two independent random variables U and V, each of which has a probability density function, the density of the product Y=UV and quotient Y=U/V can be computed by a change of variables.

Read more about this topic:  Probability Density Function

Famous quotes containing the words products, independent, random and/or variables:

    The measure discriminates definitely against products which make up what has been universally considered a program of safe farming. The bill upholds as ideals of American farming the men who grow cotton, corn, rice, swine, tobacco, or wheat and nothing else. These are to be given special favors at the expense of the farmer who has toiled for years to build up a constructive farming enterprise to include a variety of crops and livestock.
    Calvin Coolidge (1872–1933)

    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)

    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 are surprisingly few.... One can whip or be whipped; one can eat excrement or quaff urine; mouth and private part can be meet in this or that commerce. After which there is the gray of morning and the sour knowledge that things have remained fairly generally the same since man first met goat and woman.
    George Steiner (b. 1929)