Uniform Probability Distribution Calculator

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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.
continuous uniform probability distribution
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



More References and links

  1. Normal Probability Calculator
  2. Normal Distribution Problems with Solutions
  3. Elementary Statistics and Probability Tutorials and Problems
  4. Statistics Calculators, Solvers and Graphers

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