Discrete Uniform Distribution

X ~ U(a, b)

a: minimum value

b: maximum value

n: number of values = (b - a + 1)

The discrete uniform distribution is used to calculate the probability of values being in a given range (a to b) given that the probability of each outcome is the same for all outcomes.

Example

U(1,6): The probability of success is ⅙ for each outcome of the six possible outcomes.

Uniform Graph

Formulae

P(X = x) =
1
n
E(X) =
a + b
2
VAR(X) =
n 2 - 1
12

Enter the parameters for the Discrete Uniform distribution:

Minimum value: a

Maximum value: b

This calculator does the following

  • Displays the statistics for the defined distribution
  • Calculates the probabilities for a given value of x
  • Calculates the inverse for a given probability
  • Calculates the values for a hypothesis test given the significance level: H0, H1, the critical region, probability of a type I error and the probability of a type II error given the actual parameter.
  • Calculates the values for a hypothesis test given the critical region: H0, H1, the test size, the test power for the actual parameter or the power table if no parameter is specified.
  • Displays a table of probabilities for the distribution