### 数学网课代修|概率统计代写Probability and Statistics代考|MATH 1342

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学网课代修|概率统计代写Probability and Statistics代考|Theoretical Approaches

In the mathematical theory of probability, we talk of a sample space, which (in simple cases) consists of a list of the possible outcomes $(X, Y)$, seen in Table 1.1. In a theoretical treatment, we place weights of $1 / 36$ on each of the points in the space, reflecting the fact that each of the 36 points is equally likely, and then say, “What we mean by $P(X+Y=6)=\frac{5}{36}$ is that the outcomes $(1,5),(2,4),(3,3),(4,2),(5,1)$ have total weight $5 / 36$.”

Unfortunately, the notion of sample space becomes mathematically tricky when developed for more complex probability models. Indeed, it requires graduate-level math, called measure theory.

And much worse, under the sample space approach, one loses all the intuition. In particular, there is no good way using set theory to convey the intuition underlying conditional probability (to be introduced in Section 1.3). The same is true for expected value, a central topic to be introduced in Section 3.5.

In any case, most probability computations do not rely on explicitly writing down a sample space. In this particular example, involving dice, it is useful for us as a vehicle for explaining the concepts, but we will NOT use it much.

## 数学网课代修|概率统计代写Probability and Statistics代考|Our Definitions

If we were to ask any stranger on the street, “What do we mean when we say that the probability of winning some casino game is $20 \%$ “, she would probably say, “Well, if we were to play the game repeatably, we’d win $20 \%$ of the time.” This is actually the way we will define probability in this book.

The definitions here are intuitive, rather than rigorous math, but intuition is what we need. Keep in mind that we are making definitions below, not a listing of properties.

• We assume an “experiment” which is (at least in concept) repeatable. The above experiment of rolling two dice is repeatable, and even the bus ridership model is so: Each day’s ridership record would be a repetition of the experiment.

On the other hand, the econometricians, in forecasting 2009, cannot “repeat” 2008. Yet all of the econometricians’ tools assume that events in 2008 were affected by various sorts of randomness, and we think of repeating the experiment in a conceptual sense.

• We imagine performing the experiment a large number of times, recording the result of each repetition on a separate line in a note book.
• We say $A$ is an event for this experiment if it is a possible boolean (i.e., yes-or-no) outcome of the experiment. In the above example, here are some events:
\begin{aligned} &* X+Y=6 \ &* X=1 \ &* Y=3 \ &* X-Y=4 \end{aligned}
• A random variable is a numerical outcome of the experiment, such as $X$ and $Y$ here, as well as $X+Y, 2 X Y$ and even $\sin (X Y)$.

## 数学网课代修|概率统计代写Probability and Statistics代考|Our Definitions

• 我们假设一个“实验” (至少在概念上) 是可重复的。上面郑两个骰子的实验是可以重复的，就连公交车的 客流量模型也是如此：每天的客流量记录就是这个实验的重复。
另一方面，计量经济学家在预测 2009 年时，无法“重复” 2008 年。然而，计量经济学家的所有工具都假设 2008 年的事件受到各种随机性的影响，我们认为在概念上重复实验。
• 我们想象进行大量的实验，将每次重复的结果记录在笔记本的单独一行上。
• 我们说 $A$ 如果它是实验的一个可能的布尔 (即，是或否）结果，则它是该实验的事件。在上面的例子中， 这里有一些事件:
$$• X+Y=6 \quad * X=1 * Y=3 \quad * X-Y=4$$
• 随机变量是实验的数值结果，例如 $X$ 和 $Y$ 在这里，以及 $X+Y, 2 X Y$ 乃至 $\sin (X Y)$.

## 有限元方法代写

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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。