Uniform Discrete Probability Distribution

Occurs when in a single trial, all outcomes are equally likely.

• There are $n$ elements in $S$
• All outcomes $x$ have probability $P(x)=\frac{1}{n}$
• The sum of all probabilities in $S$ is $1$

Example

Random number generator between 1 and 5 inclusive.

P(X = x) = 1/5. each random number is equally likely and there is a single trial. So, this is a uniform distribution

Distribution

To get the distribution, we will make a Frequency Table first:

random number x	Probability P(X)	x * P(x)
1	1/5	1/5
2	1/5	2/5
3	1/5	3/5
4	1/5	4/5
5	1/5	5/5

Expectation

Expectation is the mean. But the formula is more suited to different cases. $\frac{1+2+3+4+5}{5}=3$