Basic probability: What Every Math Student Should Know (2nd Edition) by Henk Tijms

Author:Henk Tijms
Language: eng
Format: epub
Publisher: World Scientific Publishing Co. Pte. Ltd.
Published: 2021-08-15T00:00:00+00:00

3.5The uniform and exponential probability densities

First, we discuss in more detail the tricky and subtle concept of probability density function. A random variable X is said to be continuously distributed with probability density function f(x) if

where f(x) is a non-negative function with f(x)dx = 1 and f(x) is continuous with the possible exception of a finite number of points.20 The number f(x) is not a probability but it is a relative measure for the likelihood that the random variable X will take on a value in the immediate neighborhood of (continuity) point x:

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