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# 统计代写|统计推断代考Statistical Inference代写|STAT360 Mapping outcomes to real numbers

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## 统计代写|统计推断代考Statistical Inference代写|Mapping outcomes to real numbers

At an intuitive level, the definition of a random variable is straightforward; a random variable is a quantity whose value is determined by the outcome of the experiment. The value taken by a random variable is always real. The randomness of a random variable is a consequence of our uncertainty about the outcome of the experiment. Example 3.1.1 illustrates this intuitive thinking, using the setup described in Example 2.4.14 as a starting point.

In practice, the quantities we model using random variables may be the output of systems that cannot be viewed as experiments in the strict sense. What these systems have in common, however, is that they are stochastic, rather than deterministic. This is an important distinction; for a deterministic system, if we know the input, we can determine exactly what the output will be. This is not true for a stochastic model, as its output is (at least in part) determined by a random element. We will encounter again the distinction between stochastic and deterministic systems in Chapter 12, in the context of random-number generation.
Example 3.1.1 (Coin flipping again)

## 统计代写|统计推断代考Statistical Inference代写|Cumulative distribution functions

As mentioned above, we are usually more interested in probabilities associated with a random variable than in a mapping from outcomes to real numbers. The probability associated with a random variable is completely characterised by its cumulative distribution function.

Definition 3.2.1 (Cumulative distribution function)
The cumulative distribution function (CDF) of a random variable $X$ is the function $F_X: \mathbb{R} \longrightarrow[0,1]$ given by $F_X(x)=\mathrm{P}(X \leq x)$.
A couple of points to note about cumulative distribution functions.

1. We will use $F_X$ to denote the cumulative distribution function of the random variable $X, F_Y$ to denote the cumulative distribution function of the random variable $Y$, and so on.
2. Be warned; some texts use the argument to identify different distribution functions. For example, you may see $F(x)$ and $F(y)$ used, not to denote the same function applied to different arguments, but to indicate a value of the cumulative distribution function of $X$ and a value of the cumulative distribution function of $Y$. This can be deeply confusing and we will try to avoid doing it.

In our discussion of the properties of cumulative distribution functions, the following definition is useful.

# 统计推断代写

## 统计代写|统计推断代考统计推断代写|累积分布函数

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。