The uniform distribution is a kind of symmetric probability distribution that assigns the same chance of occurrence to each possible outcome. Because each value in the distribution has the same probability, we may say that the values are distributed uniformly. Because of the form it takes in probability distribution plots, this distribution is sometimes referred to as rectangular.
In statistics, a uniform distribution is a probability distribution in which the odds of each conceivable result occurring are identical. Because each variable has an equal chance of becoming the result, the probability remains the same.
Types of Uniform Distribution
Discrete Uniform Distribution
In stats and probability theory, a discrete uniform distribution is a statistical distribution with limited values. The probability of each occurrence characterizes it as the same. The outcomes that might occur when rolling a die with six sides is an excellent illustration of a discrete distribution that follows a consistent pattern.
One of the following numbers might be used: 1, 2, 3, 4, 5, or 6. Each of the six numbers in this particular scenario has the same probability of being drawn. Therefore, if the die with six sides is thrown, each side gets a chance equal to one-sixth of the total.
There are just so many possible values. If you roll a fair die, you will never obtain the values 1.3, 4.2, or 5.7. These numbers cannot appear on the die. If, on the other hand, another die is introduced into the mix and both are subsequently rolled, the distribution that emerges is no longer uniform since the probability of the sums is no longer the same. Another straightforward illustration of this concept is the probability distribution of a coin toss. There are only two conceivable conclusions that may be drawn from such a set of circumstances. As a result, the value of the finite set is 2.
The concept of discrete uniform distribution may be very beneficial to organizations in several different ways. For instance, it may appear in inventory management when research on the frequency of inventory sales is conducted. It can produce a probability distribution that may direct the company in the correct inventory allocation to make the most well-organized use of the available square footage.
The Monte Carlo simulation may also benefit from using a discrete uniform distribution. This modeling approach uses pre-programmed technologies to determine the likelihood of a variety of possible outcomes. The Monte Carlo method is often used for scenario forecasting and contributing to the identification of hazards.
Continuous Uniform Distribution
Not all uniform distributions are discrete; others are continuous. A continuous uniform distribution is a kind of statistical distribution that may also be referred to as a rectangle distribution. This type of distribution has an unlimited number of measurable values with an equal likelihood of being measured. Continuous random variables, as opposed to discrete random variables, can take on any actual value that falls within a specific range.
The continuous uniform distribution is most often shown in a rectangle format. An idealized random number generator is an excellent illustration of a continuous uniform distribution. Every possible outcome has the same probability of occurring in a continuous uniform distribution, just as in a discrete uniform distribution. There is an endless number of potential spots that might be present.
Examples of Uniform Distribution
Because the following outcomes also follow a uniform distribution, analysts in the actual world use the uniform distribution to simulate them.
- A game of rolling dice and flipping coins.
- The likelihood of drawing a particular card from a standard deck of playing cards.
- Because this strategy relies on all population members having the same opportunities, random sampling is used.
- When the null hypothesis is shown to be correct given a specific set of circumstances, p-values in hypothesis tests adhere to the uniform distribution.
- The uniform distribution is the one that is used by random number generators since it ensures that no number is more prevalent than the others.
- Particles that decay due to radioactive activity over time.
When there is insufficient data to predict the accurate distribution of outcomes, analysts may utilize the uniform distribution to create approximations of novel processes using the uniform distribution.
Guessing a Birthday
If you randomly approach a person and try to guess their birthday, the probability of their birthday falling precisely on the date you are supposed to follow a uniform distribution. This means that the likelihood of getting it wrong is the same regardless of which person you randomly approach.
This is because each day of the year has an equal possibility of being their birthday, or each day of the year has an equal probability of being their birthday. For example, the likelihood that 1 January is supposed to be their birthday is equal to 1/365, which is the same as the probability that 2 January is their birthday, which is the same as the probability that every day of the year is supposed to be their birthday.
In other words, the probability that 1 January is supposed to be their birthday is the same as the probability that 2 January is supposed to be their birthday.
Rolling a Dice
When a fair die is rolled, the likelihood that a number between one and six will appear on the top of the die follows a uniform distribution. This means that the probability of each number being between one and six is the same.
The likelihood that the number “one” will be shown on the top of the die is equal to 1/6, which is the same probability as the probability that the number “two” will be shown on the top of the dice, etc. As a result of the fact that each number has an equal probability of appearing at the top, the distribution may be said to be uniform.
Tossing a coin
When you flip a coin, the odds that it will land with the head facing up are precisely the same as the chances that it will land with the tail facing up. Tossing a coin is an excellent example of an activity that is considered to follow a uniform distribution since there are two possible outcomes, both of which have the same probability of materializing.
Deck of cards
The standard deck of playing cards has 52 cards, making up the total number of cards in the deck. The deck is subdivided into four sets of thirteen cards, each designated with specific shapes such as diamonds, spades, hearts, and clubs.
Since the probability of choosing a spade is equal to 0.25, which is the same as the probability of choosing a heart, diamond, or club card, the possibility that the drawn card would be either a diamond, spade, nature, or club follows a uniform distribution if you choose a card at accidental from a deck of playing cards.
This is because the probability of choosing a diamond is equal to 0.25, which is the same as the probability of selecting a club card.
Spinning A Spinner
Suppose a spinner is turned over a tray with four separate compartments while the tray is being rotated. Each room has a distinct color from the others. After being spun, there is a one in four chance that the spinner will point to one of the four colored compartments.
This probability is equal to 0.25. Therefore, it is a notable example of uniform distribution in real life since each color compartment has an equal chance of being pointed by the spinner. This makes it an excellent illustration of how uniform distribution works in practice.
Raffle Tickets
A well-known example of a uniform distribution of probabilities is a raffle. The committee in charge of organizing the event has a habit of randomly selecting one seat out of thousands of hearts and giving a prize to the individual seated in that spot.
The individuals participating in the activity purchase numbered raffle tickets, and every single one has an equal opportunity to win the prize. This is because the chance of the organizers selecting a seat as the winner is proportional to the number of seats that are still available.
Lucky Draw Contest
In a lucky draw competition, the odds of winning are the same for each individual who enters the competition and competes for a chance to win the prize. As a result, this kind of distribution is known as the uniform probability distribution, and it acquires its name from the fact the odds of winning are the same for everyone.
Throwing A Dart
Every point on the dartboard has an equal likelihood of being struck by the dart when it is thrown at the dartboard. As a result, it serves as an excellent illustration of a uniform distribution in the actual world.