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uniform (continuous) random variable
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(Definition)
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A random variable $X$ is said to be a uniform (continuous) random variable with parameters $a$ and $b$ if its probability density function is given by
and is denoted $X\sim U(a,b)$ .
Notes:
- They are also called rectangular distributions, considers that all points in the interval $[a,b]$ have the same mass.
- $E[X] = \frac{a+b}{2}$
- $Var[X] = \frac{(b-a)^2}{12}$
- $M_X(t) = \frac{e^{bt} - e^{at}}{(b-a)t}$
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"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
There are 9 references to this entry.
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 20318 times total.
Classification:
| AMS MSC: | 60-00 (Probability theory and stochastic processes :: General reference works ) |
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Pending Errata and Addenda
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![$\displaystyle f_X(x) = \frac{1}{b-a},\quad\quad x \in [a,b],$](http://images.planetmath.org:8080/cache/objects/525/js/img1.png "$\displaystyle f_X(x) = \frac{1}{b-a},\quad\quad x \in [a,b],$")