# 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 Distribution

A continuous uniform probability distribution 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