The uniform distribution function reads:

Uniform Distribution Function of a Discontinuous Random Variable

The basic characteristic of a uniform distribution is that the random variable X has an equal chance of taking any of the k values ​​X1, X2,..., Xk.

Example: Rolling a Dice

Question

A total of 6 events can occur when rolling a die, where, if the die is not biased, each number 1, 2, 3, 4, 5, or 6 has an equal chance of appearing. In this case, k = 6. The probability of getting each number is shown in the table.

1 2 3 4 5 6
1/6 1/6 1/6 1/6 1/6 1/6

The graphical appearance of the uniform distribution from the example can be shown using a bar chart.

Uniform Distribution of a Discontinuous Random Variable

The expected value of the uniform distribution is equal to

Expected value of a discrete variable corresponding to a uniform distribution

The variance of a uniform distribution is (k2-1)/12.