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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写抽样理论sampling theory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。我们的专家在代写抽样理论sampling theory方面经验极为丰富，各种代写抽样理论sampling theory相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|抽样理论作业代写sampling theory 代考|Notion of Probability

When the probability $P$ for a certain fragment of a lot to be selected is a certainty, by definition we write:
$$P=1$$
When the probability $P$ for a certain fragment of a lot not to selected is a certainty, by definition we write:
$$P=0$$
Thus, all probabilities $P$, encountered are included in a closed interval between zero and one:
$$0 \leq P_i \leq 1$$
A given probability $P$ may conveniently be expressed in percent; for example, when $P=0.1$, it is strictly equivalent to write $P=10 \%$. Note that when $P=1$, it is equivalent to write $P=100 \%$. Figure $3.1$ illustrates a typical probability distribution.

Suppose the probability distribution of all possible outcomes of the critical content $\mathrm{a}s$ of a sample collected in a lot $L$ of true unknown critical content $\mathrm{a}{\mathrm{L}}$ is known, and the distribution is represented by the sketch shown in Figure 3.1. We can then calculate any probability $P$ for $a_s$ to fall between two known or fixed limits $a_{s 1}$ and $a_{s 2}$ as follows:
$$P\left[a_{s 1} \leq a_s \leq a_{s 2}\right]=\int_{a s_1}^{a s_2} f\left(a_s\right) d a_s$$
where $\mathrm{da}{\mathrm{s}}$ is an infinitesimal constant increment and $P$ the proportion of the surface between $a{s 1}$ and $a_{s 2}$ versus the total surface of the distribution. These notions become much clearer when we draw a sketch as illustrated in Figure 3.1; probabilities and statistics are often easier to understand by drawing a simple sketch. In the same way, if $a_s$ is expressed as part of one the equation representing the total probability distribution is:
$$P\left[0 \leq a_{\mathrm{s}} \leq 1\right]=\int_0^1 f\left(a_{\mathrm{s}}\right) d a_{\mathrm{s}}=1$$
which brings us back to the meaning of equation (3.1) where $P=1$ when $100 \%$ of the surface area representing all the possible values taken by $a_s$ is considered. Note that if $a_s=1$ we are dealing with a pure constituent or mineral. There are numerous possible laws of distribution for $a_s$ and these may or may not be known. We will take a quick look at some of these distribution laws; however, we will first define the probability law of a random variable in general.

## 统计代写|抽样理论作业代写sampling theory 代考|Dependence between Random Variables

Random variables may be independent from one another. The fact that constitution heterogeneity generates short-range quality fluctuations among increments selected on a conveyor belt at regular intervals has nothing to do with fact that the same constitution heterogeneity will generate additional short-range fluctuations during subsequent sampling stages performed on the same increments. The sampling selection performed at one stage is completely independent from the sampling selection performed during other stages.

Random variables may be exclusive from one another, The fact that an analytical subsample contains the only coarse gold particle present in a sample excludes the fact that another analytical subsample selected from the sample will contain nearly as much gold; people go to ligation when they don’t understand this.

Random variables may be nonexclusive from one another. The fact that a mineral shows an important segregation taking place may or may not affect to the first order the amount of segregation generated by another mineral.

Random variables may be dependent on one another. The fact that a lot of material is showing an important constitution heterogeneity for a given constituent will be accountable for the fact that the same constituent within the same material may be affected by an important segregation.

These few comments lead to the following essential three theorems that are useful to keep in mind:

1. If random variables are independent and exclusive, the averages of their respective probability distribution are additive.
2. If random variables are independent but not exclusive, the averages of their respective probability distribution are additive; however, we shall subtract the product of these averages from the addition.
3. If random variables are dependent, the averages of their respective probability distribution are multiplicative.

This seem simple at first; however, the notion of dependence or independence between variables can rapidly become extremely complex and require in-depth study of probability laws, which is beyond our objectives.

# 抽样理论代考

## 统计代写|抽样理论作业代写sampling theory代考|概率的概念

$$P=1$$

$$P=0$$

$$0 \leq P_i \leq 1$$

$$P\left[a_{s 1} \leq a_s \leq a_{s 2}\right]=\int_{a s_1}^{a s_2} f\left(a_s\right) d a_s$$
where $\mathrm{da}{\mathrm{s}}$ 无穷小的常数增量和 $P$ 表面之间的比例 $a{s 1}$ 和 $a_{s 2}$ 相对于分布的总表面。当我们画出如图3.1所示的草图时，这些概念就变得清晰多了;通过画一个简单的草图，概率和统计通常更容易理解。同样的，如果 $a_s$ 表示为一个的一部分，表示总概率分布的方程是:
$$P\left[0 \leq a_{\mathrm{s}} \leq 1\right]=\int_0^1 f\left(a_{\mathrm{s}}\right) d a_{\mathrm{s}}=1$$
，这将我们带回等式(3.1)的意义，其中 $P=1$ 何时 $100 \%$ 表示所有可能的值 $a_s$ 被考虑。注意，如果 $a_s=1$ 我们正在处理一种纯成分或矿物。有很多可能的分布规律 $a_s$ 这些可能知道，也可能不知道。我们将快速浏览一些分布规律;然而，我们将首先定义一般随机变量的概率定律

.

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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