离散随机变量的期望值
离散随机变量的期望值是概率论中的重要概念，它表示随机变量在大量重复实验中的平均取值。通过学习本节内容，您将掌握期望值的定义、计算方法及其在实际问题中的应用。
The expected value of a discrete random variable is an important concept in probability theory that represents the average value of a random variable over a large number of repeated experiments. By studying this section, you will master the definition of expected value, its calculation methods, and its applications in practical problems.
期望值有时也称为均值，用希腊字母μ表示。本节将详细介绍如何计算单个随机变量的期望值，以及如何处理随机变量函数的期望值。
The expected value is sometimes called the mean and is denoted by the Greek letter μ. This section will detail how to calculate the expected value of a single random variable and how to handle the expected value of functions of random variables.
离散随机变量X的期望值E(X)是所有可能取值与其对应概率乘积的总和，表示随机变量的长期平均值。
The expected value E(X) of a discrete random variable X is the sum of all possible values multiplied by their corresponding probabilities, representing the long-term average value of the random variable.
期望值通过公式E(X) = ΣxP(X = x)计算，其中x是随机变量的可能取值，P(X = x)是对应的概率。
The expected value is calculated using the formula E(X) = ΣxP(X = x), where x are the possible values of the random variable and P(X = x) are the corresponding probabilities.
对于随机变量X的函数g(X)，其期望值E(g(X)) = Σg(x)P(X = x)。特别地，E(X²) = Σx²P(X = x)。
For a function g(X) of random variable X, the expected value E(g(X)) = Σg(x)P(X = x). In particular, E(X²) = Σx²P(X = x).
\[E(X) = \sum x P(X = x)\]
随机变量X的期望值等于其所有可能取值与对应概率乘积的总和。
The expected value of random variable X is equal to the sum of all its possible values multiplied by their corresponding probabilities.
\[E(g(X)) = \sum g(x) P(X = x)\]
随机变量X的函数g(X)的期望值。
The expected value of function g(X) of random variable X.
\[E(X^2) = \sum x^2 P(X = x)\]
随机变量X平方的期望值，用于计算方差。
The expected value of X squared, used for calculating variance.