Discrete Uniform Random Variable

A discrete uniform random variable is a discrete random variable for which the probability of each outcome is the same.

Example

The roll of a die is a discrete uniform random variable and has a discrete uniform probability distribution.

The random variable X can take the values X = {1, 2, 3, 4, 5, 6}

Each outcome has a probability of 1/6.

The probability distribution and cumulative distribution functions are shown below:

xi	Probability distribution, P(xi)	Cumulative Distribution, F(xi)
1	1/6	1/6 = 0.1667
2	1/6	2/6 = 0.333
3	1/6	3/6 = 0.5
4	1/6	4/6 = 0.667
5	1/6	5/6 = 0.833
6	1/6	6/6 = 1

Let’s observe a few values from the above table.

1P(3) = 1/6 or 0.1667
2
3F(3) = 0.5
4
5P(2<=X<=5) = 4\*1/6 = 0.667
6

We can generalize this as follows:

1P(x) = 1/6 or 0.1667
2
3Cumulative distribution function for any outcome i is F(xi) = i\*P(x)
4
5Probability function for a range with k outcomes = k\*P(x)
6

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Discrete Uniform Random Variable

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