#### 52.2.11 Continuous Uniform Random Variable

The continuous uniform distribution is constant over the interval [a,b] and is zero elsewhere.

Function: pdf_continuous_uniform (x,a,b)

  Returns the value at x of the density function of a \({\it ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first `load("distrib")`.

  The pdf $$ f(x; a, b) = \cases{ \displaystyle{1\over b-a} & for $0 \le x \le 1$ \cr \cr 0 & otherwise } $$

  and is 0 otherwise.

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Function: cdf_continuous_uniform (x,a,b)

  Returns the value at x of the distribution function of a \({\it ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first `load("distrib")`.

  The cdf is $$ F(x; a, b) = \cases{ 0 & for $x < a$ \cr \cr \displaystyle{x-a\over b-a} & for $a \le x \le b$ \cr \cr 1 & for $x > b$ } $$

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Function: quantile_continuous_uniform (q,a,b)

  Returns the q-quantile of a \({\it ContinuousUniform}(a,b)\) random variable, with a<b; in other words, this is the inverse of `cdf_continuous_uniform`. Argument q must be an element of [0,1]. To make use of this function, write first `load("distrib")`.

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Function: mean_continuous_uniform (a,b)

  Returns the mean of a \({\it ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first `load("distrib")`.

  The mean is $$ E[X] = {a+b\over 2} $$

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Function: var_continuous_uniform (a,b)

  Returns the variance of a \({\it ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first `load("distrib")`.

  The variance is $$ V[X] = {(b-a)^2\over 12} $$

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Function: std_continuous_uniform (a,b)

  Returns the standard deviation of a \({\it ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first `load("distrib")`.

  The standard deviation is $$ D[X] = {b-a \over 2\sqrt{3}} $$

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Function: skewness_continuous_uniform (a,b)

  Returns the skewness coefficient of a \({\it ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first `load("distrib")`.

  The skewness coefficient is $$ SK[X] = 0 $$

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Function: kurtosis_continuous_uniform (a,b)

  Returns the kurtosis coefficient of a \({\it ContinuousUniform}(a,b)\) random variable, with a<b. To make use of this function, write first `load("distrib")`.

  The kurtosis coefficient is $$ KU[X] = -{6\over5} $$

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Function: random_continuous_uniform (a,b)
`random_continuous_uniform` (a,b,n)

  Returns a \({\it ContinuousUniform}(a,b)\) random variate, with a<b. Calling `random_continuous_uniform` with a third argument n, a random sample of size n will be simulated.

  This is a direct application of the `random` built-in Maxima function.

  See also `random`. To make use of this function, write first `load("distrib")`.

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