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uniform (continuous) random variable

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A random variable is said to be a uniform (continuous) random variable with parameters and if its probability density function is given by

$\displaystyle f_X(x) = \frac{1}{b-a},\quad\quad x \in [a,b],$

and is denoted $X\sim U(a,b)$ .

Notes:

They are also called rectangular distributions, considers that all points in the interval have the same mass.
$E[X] = \frac{a+b}{2}$
$Var[X] = \frac{(b-a)^2}{12}$
$M_X(t) = \frac{e^{bt} - e^{at}}{(b-a)t}$

"uniform (continuous) random variable" is owned by mathcam. [ full author list (2) | owner history (1) ]

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Other names:

uniform random variable, rectangular distribution, uniform distribution

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Cross-references: mass, interval, points, probability density function, parameters, random variable
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This is version 5 of uniform (continuous) random variable, born on 2001-10-26, modified 2006-10-25.
Object id is 525, canonical name is UniformContinousRandomVariable.
Accessed 16781 times total.

Classification:

60-00 (Probability theory and stochastic processes :: General reference works )

Pending Errata and Addenda

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