Uniform Random Variable

Uniform Random Variable

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable. The probability distribution function for this random variable is: $$ F_X(x) = \frac{x-a}{b-a} $$ where $b$ and $a$ are parameters that give the highest and lowest (real) values that the random variable can take. The probability density function for this random variable is: $$ f_X(x) = \frac{1}{b-a} $$ and the expectation and variance are $\mathbb{E}(X) = \frac{1}{2}(a+b)$ and $\textrm{var}(X) = \frac{1}{12}(b-a)^2$.

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