Uniform distribution is a word used in statistics to describe a type of probability distribution in which every conceivable outcome has an equal chance of occurring. Because each variable has an equal chance of being the outcome, the probability is constant.

## Continuous Uniform Distribution

## Example

### History/Origin

### Types of Uniform Distribution

**Discrete:**A discrete uniform distribution is a statistical distribution with limited values and equal probability of outcomes in statistics and probability theory. The multiple results of rolling a 6-sided die are a nice example of a discrete uniform distribution. 1, 2, 3, 4, 5, or 6 are examples of possible values. Each of the six numbers has an equal chance of occuring in this situation. As a result, each side of the 6-sided die has a 1/6 probability each time it is thrown. The total number of possible values is limited. When rolling a fair die, it is impossible to acquire a value of 1.3, 4.2, or 5.7. When a second die is added and both are thrown, the resulting distribution is no longer uniform because the probability of the sums is not equal. The probability distribution of a coin flip is another simple example. There can only be two conceivable outcomes in such a circumstance. As a result, the finite value is two.

**Continuous:**A statistical distribution with an infinite number of equally likely measurable values is known as a continuous uniform distribution (sometimes known as a rectangle distribution). A continuous random variable, unlike discrete random variables, can take any real value within a given range.

A rectangular shape is typical for a continuous uniform distribution. An idealized random number generator is a nice example of a continuous uniform distribution. Every variable has an equal chance of occurring in a continuous uniform distribution, just as it does in a discrete uniform distribution. However, there are an endless number of possible points.

### Properties

- The mean of the distribution is .
- The median of the distribution is .
- The variance of the distribution is (b-a)∧2/12.
- The mode of the distribution is any value of.
- The skewness of the distribution is 0.
- The kurtosis of the distribution is .

### Special characteristics of Uniform distribution

- The probability of this distribution is same for equal intervals in any part of the distribution.
- The probability of uniform distribution depends on the length of the intervals, not on its position.
- The pdf of the uniform distribution over the interval [0,1] is defined by f(x)=1.
- Moreover, uniform distribution can be defined in a infinite number of ways.

### Uniform Vs. Normal Distribution

### Applications

A conventional deck of cards contains 52 cards. Hearts, diamonds, clubs, and spades are the four suits of the deck. A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, and two jokers make up each suit. For this example, we’ll ignore the jokers and face cards, focusing solely on the number cards that are duplicated in each suit. As a result, we’re left with 40 cards, which are a collection of discrete data.

Let’s say you want to know how likely it is to get a 2 of hearts from the changed deck. The chances of getting a 2 of hearts are 1 in 40 or 2.5 percent. Because each card is unique, the chances of you pulling any of the cards in the deck are the same.