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:

    “All that is told of the sea has a fabulous sound to an inhabitant of the land, and all its products have a certain fabulous quality, as if they belonged to another planet, from seaweed to a sailor’s yarn, or a fish story. In this element the animal and vegetable kingdoms meet and are strangely mingled.”
    —Henry David Thoreau (1817–1862)

    “Where beauty is worshipped for beauty’s sake as a goddess, independent of and superior to morality and philosophy, the most horrible putrefaction is apt to set in. The lives of the aesthetes are the far from edifying commentary on the religion of beauty.”
    —Aldous Huxley (1894–1963)

    “... the random talk of people who have no chance of immortality and thus can speak their minds out has a setting, often, of lights, streets, houses, human beings, beautiful or grotesque, which will weave itself into the moment for ever.”
    —Virginia Woolf (1882–1941)

    “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)