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In statistics, a uniform distribution refers to a probability distribution in which all outcomes are equally likely to occur. Probability distributions can help you judge the likelihood of future events.
In statistics, a uniform distribution refers to a probability distribution in which all outcomes are equally likely to occur. Probability distributions can help you judge the likelihood of future events.
For example, when drawing a deck of playing cards, the likelihood of drawing a heart, club, diamond, or spade is equally likely, so a uniform distribution of playing cards is to be expected. A coin toss is also an example of a uniform distribution because when a coin is tossed, the probability of heads or tails is the same.
A uniform distribution can be viewed as a horizontal straight line. Taking a coin toss as an example, the probability of heads or tails is 50% (p = 0.50). When plotted on a chart, the y-axis value is 0.50.
There are two types of uniform distributions: discrete and continuous.
The results of rolling a die provide an example of a discrete uniform distribution. Possible results are 1, 2, 3, 4, 5 or 6, but it is impossible to roll 2.3, 4.7 or 5.5. Therefore, the throw of the dice generates a discrete distribution, with each outcome having a probability of 1/6. With only 6 possible return values and no other values in between, the possibilities are limited.
In contrast, a continuous uniform distribution has unlimited distribution possibilities. An idealized random number generator can be viewed as a continuous uniform distribution. For this distribution, every point between 0.0 and 1.0 has the same chance of appearing, and the points within this interval are infinite.
There are many other important continuous distributions, such as the normal distribution, chi-square distribution, and Student's t distribution.
Additionally, there are several distribution-related data generation or data analysis functions that help explain variables and their variance in a data set. These functions include probability density functions, cumulative densities, and moment generating functions.
Tip: The term "discrete" in statistics refers to a variable that has a single countable and finite number of possible values.
Distributions are a simple way to visualize a set of data. It can be displayed in the form of a chart or a list, showing the probability of different values of a random variable occurring. The uniform distribution is perhaps the simplest of all probability distributions.
In a uniform distribution, all possible values have the same probability of occurring. When displayed as a bar or line chart, this distribution has the same height for each possible outcome. This way, its shape looks like a rectangle, so it is sometimes called a rectangular distribution.
Taking the drawing of a certain suit of poker cards as an example, the random chances of drawing hearts and drawing spades are the same, both 1/4 or 25%.
Rolling the dice will produce one of the numbers 1, 2, 3, 4, 5 or 6. Since there are only 6 possible outcomes, the probability of rolling any one of them is 16.67% (1/6). When plotted on a chart, each possible outcome is fixed on the x-axis and represented by a probability value on the y-axis.
There are 52 standard playing cards in total, including four suits: hearts, diamonds, clubs and spades. Each suit contains A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, and K. Also, this deck also has 2 Joker cards, but in this example we will ignore the Joker and Face cards and focus only on the number cards in each suit. Therefore, we are left with 40 cards, forming a discrete set of data.
Suppose you want to know the probability of drawing a 2 of hearts from this modified hand. The probability of drawing a 2 of hearts is 1/40 or 2.5%. Each card is unique, so the probability of drawing any one from the deck is equal.
Now, let's consider the probability of drawing a heart from the deck. The probability is significantly higher. Why? Because now we only focus on the suits in the deck. Since there are only four suits, the probability of drawing a heart is 1/4 or 25%.
Note: The result plot of a die roll will be discretely uniform, while the results (mean) of multiple rolls (multiple dice) will be normally distributed.
Some of the most common probability distributions include:
Perhaps the most familiar and widely used is the normal distribution, which is often represented by a bell-shaped curve. The normal distribution shows the distribution of continuous data and centers most of the data at or near the mean.
In the normal distribution, the area under the curve is equal to 1, and 68.27% of the data falls within 1 standard deviation of the mean (the degree of data dispersion); 95.45% of the data falls within 2 standard deviations of the mean, and about 99.73% of the data falls within 3 standard deviations of the mean. As data points move away from the mean, the frequency of occurrence decreases.
A discrete uniform distribution states that variables within a range have the same probability of occurrence. There is no variation in its possible outcomes, and the data is discrete, not continuous. The shape is similar to a rectangle rather than the bell shape of a normal distribution. Still, the area under the graph is equal to 1.
A uniform distribution is a probability distribution that states that the likelihood of an outcome in a discrete data set is the same for every value.
The formula for discrete uniform distribution is:
<!-- @@@ -->No, the uniform distribution is not normal. Normal distribution refers to the distribution of data around the mean, indicating that the probability of a variable occurring near the mean is higher than the probability of occurring far from the mean. The probability of occurrence of normal data is not uniform, but the probability of occurrence of uniform distribution is consistent.
The expectation of a uniform distribution is that all possible outcomes have the same probability. The probability of one variable is the same as the probability of another variable.
The uniform distribution is one example of many probability distributions in statistics. A uniform distribution is a distribution in which all possible outcomes are finite and equally likely to occur. For example, rolling a die presents only six possible outcomes, each with a probability of ⅙.
[1] National Institute of Standards and Technology. "What Do We Mean by "Normal" Data?"
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否，均匀分布不是正态的。正态分布指数据围绕均值的分布情况，说明变量在均值附近发生的概率高于远离均值发生的概率。正态数据的发生概率不是均匀的，而均匀分布的发生概率是一致的。
均匀分布的期望是所有可能结果拥有相同的概率。一个变量的概率与另一个变量的概率相同。
均匀分布是统计学中多种概率分布的示例之一。均匀分布是所有可能结果都是有限的且发生概率相等的分布。例如，掷一个骰子只会呈现六种可能的结果，每一种结果发生的概率都是⅙。
[1] National Institute of Standards and Technology. "What Do We Mean by "Normal" Data?"
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