Uniform distribution is a form of probability distribution in which an event is equally likely to occur within a certain interval. The random variable used in uniform distribution is a continuous random variable, which is plotted along the x-axis. A continuous random variable is said to follow a uniform distribution if the amplitude of the uniform distribution function remains constant between a certain range, say a and b, and is zero otherwise. The area under the curve of a probability distribution function is always equal to one, therefore the value of the amplitude is equal to the reciprocal of the length of the range of the continuous random variable in consideration. The shape of the graph of a uniform distribution closely resembles a rectangle geometric figure, which is why it is also known as rectangular distribution.
Types of Uniform Distribution
On the basis of types of possible outcomes of an experiment, uniform distribution can be divided into two broad categories:
1. Discrete Uniform Distribution
A discrete uniform distribution refers to a type of statistical and probability distribution where the probability of occurrence of the events is equally likely and falls within a finite set of values. Some of the examples of a discrete uniform distribution include rolling a six-faced fair die, flipping a coin, etc. The concept of discrete uniform distribution is very helpful in business and management. It can be used to form probability distribution to guide a firm on how to use the resources in the best possible way. Discrete uniform distribution is also applicable to Monte Carlo simulation, which is further helpful in applications such as forecasting and early recognition of risks.
2. Continuous Uniform Distribution
Continuous uniform distribution is a statistical and probability distribution that has an infinite number of equally likely values. Such a uniform distribution can take any real value within the specified range as an output. The example of a continuous uniform distribution includes a random number generator.
Examples of Uniform Distribution
1. Guessing Birthday
If you randomly approach a person and try to guess their birthday, the probability of their birthday falling exactly on the date you have guessed follows a uniform distribution. This is because every day of the year has equal chances of being his/her birthday or every day of the year is equally likely to be his/her birthday. For instance, the probability that the 1st of January is supposed to be his/her birthday is equal to 1/365, which is the same as the probability that the 2nd of January is his/her birthday, which is the same as the probability of each and every day of the year to be his/her birthday.
2. Rolling a Dice
When a fair die is rolled, the probability that the number appearing on the top of a die lies in between one to six follows a uniform distribution. The probability that number ‘one’ will appear on the top of the die is equal to 1/6, which is the same as the probability that number ‘two’ will appear on the top of the die, and so on. Each number has equal chances of occurring on the top hence, the distribution is uniform in nature.
3. Tossing a Coin
When you flip a coin, the probability of the coin landing with a head faced up is equal to the probability that it lands with a tail faced up. Since the experiment of tossing the coin has two outcomes each of which is equally likely to occur, it is said to be following a uniform distribution.
4. Deck of Cards
The total number of cards present in the deck of playing cards is equal to 52. The deck is further divided into four sets of 13 cards each of which is marked with certain shapes including diamond, spade, heart, and club. If you select a card randomly from a fair deck of playing cards, the probability that the drawn card would be either a diamond, spade, heart, or club follows a uniform distribution because the probability of choosing a spade is equal to 0.25, which is same as the probability of choosing a diamond, heart, or a club card.
5. Spinning a Spinner
Suppose a spinner is rotated over a tray that consists of four individual compartments. Each of the compartments is coloured different from each other. The probability that the spinner after spinning would point towards any of the four coloured compartments is equal to 0.25. Hence, it forms a prominent example of uniform distribution in real life because each colour compartment has equal chances to be pointed by the spinner.
6. Raffle Tickets
A raffle is a prominent example of a uniform probability distribution. The event’s organising committee tends to select a particular seat out of thousands of seats and reward the person sitting on it with a prize. The people participating in the event buy numbered raffle tickets and each of them possesses an equal chance at winning. This is because the probability of a seat being chosen by the organisers as the winner is equal to the probability of every other seat being chosen.
7. Lucky Draw Contest
The probability of a person winning a lucky draw contest is equal to the winning probability of every other person participating in the same event. Hence, such a distribution is known as the uniform probability distribution because the chances of every person winning are equal.
8. Throwing a Dart
When you throw a dart at the dartboard, each and every point of the dartboard has an equal probability of getting hit by it. Hence, it is a prime example of uniform distribution in real life.