What Is a Uniform Distribution?

In statistics, probability distributio🧔ns can help you decide the probability of a future event—that is, the likelihood of something happening. A uniform distribution is a type of probability distribution where all outcomes are equally likely.

A deck of cards is expected to have a uniform distribution because the lik𓆏elihood of drawing a heart, a club, a diamond, or a spade is equally likely. A coin also has a uniform distribution expectation because the odds of getting either h𓄧eads or tails is the same.

A uniform distribution can be visualized as a straight horizontal line. For a coin flip, heads or tails each has a probability of occurring 50% of the time (p = 0.50), so it would be plotted on a chart with a line from the y-axis at 0.50.

Understanding Uniform Distributions

There are two types of uniform distributions: discrete and continuous.

Discrete Uniform Distributions

The 𒆙possible results of rolling a die provide an example of a discrete uniform distribution. It is possible to roll a 1, 2, 3, 4, 5, or 6, but it is not possible to roll, for example, a 2.3, 4.7, or 5.5. Therefore, the roll of a die generates a discrete distribution with the probability of 1/6 for each outcome. There are only 6 possible values to return and nothing in between. The possibilities are finite.

Continuous Uniform Distributions

𓆉 Continuous uniform distributions have infinite distribution possibilities. An idealized random 🥃number generator would be considered a continuous uniform distribution. With this type of distribution, every point in the continuous range between 0.0 and 1.0 has an equal opportunity of appearing, yet there is an infinite number of points between 0.0 and 1.0.

There are several other important continuous distributions, such as the normal distribution, chi-square, and Student's 澳洲幸运5官方开奖结果体彩网:t-distribution.

Distribution Analysis

There are also several data generating or data analyzing functions associated with distributions that help explain the variables and their variance within a data set. These functions include 澳洲幸运5官方开奖结果体彩网:probability density function, cumulꦰative density, and moment generating functions.

Visualizing Uniform Distributions

A distribution is a simple way to visualize a set of data. It can be shown either as a graph or a list, and reveals which𒆙 values of a random variable have lower or higher chances of happening.

In a uniform distribution, each value in the set of possible values has the same possibility of happening. When displayed as a bar or line graph, this distribution has the same height for each potential outcome. In this way, it can look like a 澳洲幸运5官方开奖结果体彩网:rectangle and therefore is sometimes described as the rectܫangular dis♛tribution.

If you think about the✤ possibility of drawing a particular suit from a deck of playing cards, there is a random yet equal chan🌞ce of pulling a heart as there is for pulling a spade—that is, 1/4 or 25%. (There are four suits.)

The roll of a die yields one of six numbers: 1, 2, 3, 4, 5, or 6. Because there are only 6 possible outcomes, the probability of you landing on any one of them is 16.67% (1/6). When plotted on a graph, the distribution is represented as a horizontal line, witℱh each possﷺible outcome captured on the x-axis, at the fixed point of probability along the y-axis.

Example of a Uniform Distribution

There are 52 cards in a traditional deck of cards. Also in that deck are four suits: hearts, diamonds, clubs, and spades. Each suit contains an ace, two, three, four, five, six, seven, eight, nine, 10, jack, queen, and a king. The deck contains two jokers, as well. However, we'll ignore the jokers and face cards for this example, and focus only on number cards replicated in each suit. As a result, we are left with 40 cards, a set of discrete data.

Suppose you want to know the probability of pulling a two of hearts from the m🦂odified deck. The probability of pulling a two of hearts is 1/40 or 2.5%. Each card is unique. Therefore, the likelihood that you will pull any one of the cards in the deck is the same.

Now, let's consider the likelihood of pulling a heart from the deck. The probability is significantly higher. Why? We are now only concerned with the suits in the deck. Since there are four suits and each suit has the same number of cards, pulling a heart yields a probability of 1/4 or 25%.

Uniform Distribution vs. Normal Distribution

Some of the mos𒆙t common probability distributions a𝔍re:

• Discrete uniform
• Binomial
• Continuous uniform
• Normal
• Exponential

Normal

One of the most widely used distributions is the 澳洲幸运5官方开奖结果体彩网:normal distribution, which is often depicted as a 澳洲幸运5官方开奖结果体彩网:bell curve. Normal distributions show how continuous data is distributed and depict most of the data as concentrated on the mean (average).

In a normal distribution, the area under the curve equals one. 68.27% of all data falls within one standard deviation (how dispersed the numbers are) from the mean. 95.45% of all data falls within two standard deviations from the mean, and approximately 99.73% of all data falls within three standard deviations from the mean. As the data points move away from the 🐓mean, the frequency of data occurring decreases.

Uniform

Discrete uniform distribution shows that variables in a range have the same probability of occurring. There are no variations in probable outcomes and the data is discrete, rather than continuous. Its shape resembles a rectangle, rather than the normal distribution's bell. Like a normal distribution, however, the area under the graph is equal to one.

Explain Uniform Distribution Like I'm Five

With a uniform distribution, you are just as likely to get one outcome as another. Take a die with six sides, for example. You're just as likely to roll a 1 as you are to roll a 2 (or 3, 4, 5, or 6).

The Bottom Line

A uniform distribution is a type of probability distribution that is used in statistics. A uniform, or rectangular, distribution is one where all possible outcꦺomes are finite and equally likely to occur. For example, the roll of a single die presents just six possible results and each result has a ⅙ chance of taking place.