## What is Uniform Distribution?

A uniform random variable is the simplest continuous random variable. A uniform distribution assumes that every value between [a, b] has an equal chance of occurring. The Probability Density Function (PDF) of a uniform random variable does not depend on y because all values are equally likely.

### PDF of Uniform Distribution:

$ f(Y)_{Y} = \frac{1}{b-a} $

### CDF of Uniform Distribution:

The CDF returns the cumulative probability of observing a value less than or equal to the argument and is:

$ F_{y}(y) = \left\{\begin{matrix}

o & & \\ \frac{y-a}{b-a}

& & \\

1\end{matrix}\right. $

The CDF is 0 to the left of a, which is the smallest value that could be produced, linearly increases from a to b, and then is 1 above b. When a = 0 and b = 1, the distribution is called the standard uniform.

There are 52 cards in a traditional deck of cards. In it are four suits: hearts, diamonds, clubs, and spades.

Each suit contains an A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, and two jokers. However, we’ll do away with the jokers and face cards for this example, focusing only on number cards replicated in each suit. As a result, we are left with 40 cards, a discrete data set.

## Why is Uniform Distribution important?

The uniform distribution is important because it is arguably the most straightforward distribution. Several processes follow uniform distribution, which assists risk professionals in assessing its probabilities and likelihoods.