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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写统计推断Statistical inference方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写统计推断Statistical inference代写方面经验极为丰富，各种代写统计推断Statistical inference相关的作业也就用不着说。

• 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

## 统计代写|统计推断代写Statistical inference代考|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 $F_X(x)=\mathrm{P}(X<x)$.
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.
Definition 3.2.2 (Right continuity)
A function $g: \mathbb{R} \rightarrow \mathbb{R}$ is right-continuous if $g(x+)=g(x)$ for all $x \in \mathbb{R}$, where $g(x+)=\lim _{h \downarrow 0} g(x+h)$.

The notation $g(x+)$ is used for limit from the right. There is nothing complicated about this; it is just the limit of the values given by $g$ as we approach the point $x$ from the right-hand side. Right continuity says that we can approach any point from the right-hand side without encountering a jump in the value given by $g$. There is an analogous definition of left continuity in terms of the limit from the left; $g$ is left-continuous if $g(x-)=\lim {h \downarrow 0} g(x-h)=g(x)$ for all $x$. Somewhat confusingly, the notation $\lim {h \uparrow 0}$ is sometimes used. This is discussed as part of Exercise 3.2.
The elementary properties of cumulative distribution functions are inherited from their definition in terms of probability. It is true, but rather harder to show, that any function satisfying the three properties given in Proposition 3.2.3 is the distribution function of some random variable. We will only prove necessity of the three conditions.

## 统计代写|统计推断代写Statistical inference代考|Discrete and continuous random variables

Any function satisfying the properties given in Proposition $3.2 .3$ is a cumulative distribution function. The general theory associated with functions of this type is rather technical. For the most part we restrict our attention to two classes of random variable and the associated distributions. These classes are referred to as discrete and continuous.

Discreteness and continuity are properties that we attribute to random variables and their distributions. In other words, these are properties of our models for real phenomena. The issue of whether the world is fundamentally discrete or continuous was a preoccupation of ancient philosophers, a preoccupation that led, among other things, to Zeno’s paradoxes. If you ask a modern philosopher, they might say “the world is both continuous and discrete” which is to say “both are useful models”; this is a good answer. In the situations encountered by practising statisticians, it is usually fairly easy to determine whether a discrete or continuous variable should be used. In many instances, it is convenient to use a continuous random variable to model situations that are clearly discrete. The ideas developed for dealing with discreteness and continuity are also useful when the situation demands a variable that is neither continuous nor discrete. Before we give the formal definitions, it is useful to consider some examples illustrating the distinction between continuity and discreteness. As an initial attempt, we may define discreteness as a property that we attribute to things that we can count, and continuity as being associated with things that we measure.
Example 3.3.1 (Appropriateness of discrete or continuous models)

1. Discrete model: Hurricanes develop in the Atlantic Basin and generally move westwards towards North America. We will assume that the rules for classification of hurricanes are clear cut, and that the equipment used to perform measurements is accurate (this is not too far from the truth). Suppose that we want a model for the number of hurricanes that develop each year. We know that the number of hurricanes will turn out to be a natural number, $0,1,2, \ldots$, and that we cannot have any values in between. This is a candidate for modelling using a discrete random variable.
2. Continuous model: Suppose that I snap a matchstick. By eye we could probably judge the distance between the bottom of the match and the break to within $5 \mathrm{~mm}$. To get a more accurate measurement, we could use a ruler. A ruler would be accurate to within, say, $0.5 \mathrm{~mm}$. If we were still not happy, we might use a more accurate device; for example, a micrometer would give us a reading accurate to around $0.01 \mathrm{~mm}$. The point here is that we treat length as a continuous scale; that is, we can measure length to any degree of accuracy, given a sufficiently sophisticated device. Thus, the length of a snapped match is a candidate for modelling using a continuous random variable.

# 统计推断代考

## 统计代写|统计推断代写统计推断代考|累积分布函数

.

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$g(x+)$表示从右开始的极限。这一点也不复杂;当我们从右边接近$x$点时，它只是$g$给出的值的极限。右连续性表示我们可以从右边接近任何点，而不会遇到$g$给出的值的跳跃。关于左连续性有一个类似的定义即从左开始的极限;如果$g(x-)=\lim {h \downarrow 0} g(x-h)=g(x)$对于所有$x$，则$g$是左连续的。有些令人困惑的是，有时使用符号$\lim {h \uparrow 0}$。这将作为练习3.2的一部分进行讨论。累积分布函数的基本性质继承自它们在概率方面的定义。确实，但很难证明，任何满足命题3.2.3中给出的三个性质的函数都是某个随机变量的分布函数。我们将只证明这三个条件的必要性

## 统计代写|统计推断代写统计推理代考|离散和连续随机变量

. 任何满足命题$3.2 .3$中给出的性质的函数都是一个累积分布函数。与这类函数有关的一般理论是相当技术性的。在大多数情况下，我们将注意力限制在两类随机变量及其相关分布上。这些类被称为离散类和连续类 离散性和连续性是我们归因于随机变量及其分布的属性。换句话说，这些是真实现象模型的特性。世界在本质上是离散的还是连续的，这个问题是古代哲学家们所关心的问题，这个问题导致了芝诺悖论的产生。如果你问现代哲学家，他们可能会说”世界既是连续的又是离散的”也就是说”两者都是有用的模型”这是一个很好的回答。在从事统计工作的人员所遇到的情况中，通常很容易确定应该使用离散变量还是连续变量。在许多情况下，使用连续随机变量来模拟明显离散的情况是很方便的。当情况需要一个既非连续也非离散的变量时，为处理离散性和连续性而发展起来的思想也很有用。在给出正式定义之前，考虑一些例子来说明连续性和离散性之间的区别是有用的。作为最初的尝试，我们可以将离散性定义为我们可以计算的事物的属性，将连续性定义为与我们度量的事物相关的属性。例3.3.1(离散或连续模型的适当性)

1. 离散模式:飓风在大西洋盆地形成，一般向西向北美移动。我们将假设飓风的分类规则是明确的，用于进行测量的设备是准确的(这与事实相差不远)。假设我们想要一个每年形成飓风数量的模型。我们知道飓风的数量将会是一个自然数，$0,1,2, \ldots$，我们不可能有任何介于两者之间的数值。这是一个使用离散随机变量建模的候选模型。
2. 连续模型:假设我折断火柴棒。凭肉眼，我们大概可以判断出比赛底部和突破点之间的距离在$5 \mathrm{~mm}$以内。为了得到更精确的测量，我们可以使用尺子。尺子可以精确到$0.5 \mathrm{~mm}$以内。如果我们仍然不快乐，我们可以使用更精确的仪器;例如，千分尺可以给我们精确到$0.01 \mathrm{~mm}$左右的读数。这里的要点是，我们将长度视为一个连续的刻度;也就是说，我们可以测量长度到任何程度的准确性，只要一个足够复杂的设备。因此，折断匹配的长度是使用连续随机变量建模的候选值

## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师