# Uniform Probability Distribution Calculator

   

An online calculator that calculates the mean, standard deviation and probability of a continuous uniform probability distribution is presented. A second calculator that calculates $x_1$ (inverse problem) such that $P(X \lt x_1) = p$ given $p$ is also included.

## Continuous Uniform Probability Ditribution

A continuous uniform probability ditribution has the probability density function of the form
$f(x) = \begin{cases} \dfrac{1}{b-a} \quad \text{for} \quad a \le x \le b \\ \\ 0 \quad \text{for} \quad x \lt a \quad \text{or} \quad x \gt b \\ \end{cases}$
and whose graph is shown below.

The probability that the random variable $X$ is less than $x_1$ is given by $\displaystyle P(X \lt x_1) = \int_{a}^{x_1} \dfrac{1}{b-a} \; dx$
The mean, variance and standard deviation of a continuous uniform probability distribution, as defined above, are given by:
Mean = $\dfrac{1}{2}(a +b)$
Variance = $\dfrac{(b-a)^2}{12}$
Standard Deviation = $\sqrt{\dfrac{(b-a)^2}{12}}$
We present two calculators.

## 1 - Find the mean, standard deviation and probability $P(X \lt x_1)$ given $a , b$ and $x_1$

$a$ = ,      $b$ = ,     $x_1$ =

Decimal Places =

Output

## 2 - Inverse Problem: Find $x_1$ such that $P(X \lt x_1) = p$ given $a , b$ and $p$:

$a$ = ,      $b$ = ,     $p$ =

Output