distribution function

简明释义

分布函数

英英释义

例句

1.In statistics, the distribution function 分布函数 helps us understand how probabilities are distributed across different outcomes.

在统计学中，分布函数 distribution function 帮助我们理解概率是如何在不同结果中分布的。

2.To model the data accurately, we need to identify the appropriate distribution function 分布函数 for our sample.

为了准确建模数据，我们需要为我们的样本确定适当的 分布函数 distribution function 。

3.In finance, the normal distribution function 分布函数 is often used to model asset returns.

在金融中，正态 分布函数 distribution function 通常用于模拟资产回报。

4.The distribution function 分布函数 can be used to calculate the expected value of a random variable.

可以使用 分布函数 distribution function 来计算随机变量的期望值。

5.The cumulative distribution function 分布函数 gives the probability that a random variable is less than or equal to a certain value.

累积分布函数 distribution function 给出了随机变量小于或等于某个值的概率。

作文

In the field of statistics and probability theory, the concept of a distribution function is fundamental for understanding how random variables behave. A distribution function (分布函数) provides a way to describe the probabilities associated with the values that a random variable can take. It is a mathematical function that gives the probability that a random variable is less than or equal to a certain value. This is crucial for both theoretical and applied statistics, as it allows researchers to make inferences about populations based on sample data.To illustrate the importance of the distribution function (分布函数), consider a simple example involving a six-sided die. When we roll the die, the outcome can be any integer from 1 to 6. The distribution function for this scenario would assign a probability to each possible outcome. For a fair die, the probability of rolling any specific number is 1/6. Therefore, the distribution function can be defined as follows: P(X ≤ x) = 0 for x < 1, P(X ≤ x) = 1/6 for 1 ≤ x < 2, P(X ≤ x) = 2/6 for 2 ≤ x < 3, and so on, until P(X ≤ x) = 1 for x ≥ 6.This example highlights how the distribution function (分布函数) helps us understand the likelihood of different outcomes. In more complex situations, such as when dealing with continuous random variables, the distribution function takes on a slightly different form. Instead of assigning probabilities to individual outcomes, it describes the cumulative probability up to a certain point. For instance, the normal distribution, which is widely used in statistics, has a characteristic bell-shaped curve and its distribution function is defined using the mean and standard deviation of the data.Understanding the distribution function (分布函数) is essential for various statistical methods, including hypothesis testing, confidence intervals, and regression analysis. By knowing the distribution function, we can determine how likely it is to observe a particular result given a set of assumptions about the underlying population.Moreover, the distribution function (分布函数) plays a crucial role in fields such as finance, engineering, and social sciences. For example, in finance, the distribution function is used to model stock prices and assess risk. In engineering, it can help predict failure rates of components based on historical data. In social sciences, researchers use distribution functions to analyze survey data and understand behavioral patterns.In conclusion, the distribution function (分布函数) is a vital concept in statistics that allows us to quantify uncertainty and make informed decisions based on data. Whether dealing with discrete or continuous variables, the distribution function provides a framework for understanding the probabilities associated with different outcomes. As we continue to collect and analyze data in various fields, mastering the concept of the distribution function will remain an essential skill for researchers and practitioners alike.