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# 统计代写|非参数统计代写Nonparametric Statistics代考|STAT6610 Chapter Overview

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## 统计代写|非参数统计代写Nonparametric Statistics代考|BASIC PROBABILITY

The term probability indicates how likely an event is or what the chance is that the event will happen. Most events can’t be predicted with total certainty; the best we can do is say how likely they are to happen, and quantify that likelihood or chance using the concept of probability. A probability is a real number between (and including) zero and one. When an event is certain to happen, its probability equals one, whereas when it is impossible for the event to happen, its probability equals zero. Otherwise, the event is likely to happen or occur with a certain probability, expressed as a fraction between zero and one. For example, when a coin is tossed, there are two possible outcomes, namely, that a head (H) or a tail (T) can be observed. Note that an outcome is the result of a single trial of an experiment and the sample space $(S)$ constitutes all possible outcomes of an experiment (the sample space is exhaustive). In the coin tossing example, the sample space is given by $\mathrm{S}={\mathrm{H}, \mathrm{T}}$. If the coin is unbiased (or fair), the probability $(P)$ of observing a head is the same as the probability of observing a tail, each of which equals $\frac{1}{2}$. The probability of the set of all possible experimental outcomes in the sample space must equal one. In this example, this is evident since $P(\mathrm{H})+P(\mathrm{~T})=0.5+0.5=1$. When all experimental outcomes in the sample space are equally likely, this is referred to as the classical method of assigning probabilities, which is illustrated in the coin example. Another example of the classical method of assigning probabilities is when a dice is thrown. In this case, the sample space is given by $\mathrm{S}={1,2,3,4,5,6}$ and if the dice is unbiased (or fair) the probability of observing a one on the dice is the same as observing any other value on the dice that equals $\frac{1}{6}$. Mathematically, we can write
$$\mathrm{P}\left(\mathrm{E}{1}\right)=\frac{1}{6} \quad \mathrm{P}\left(\mathrm{E}{2}\right)=\frac{1}{6} \quad \mathrm{P}\left(\mathrm{E}{3}\right)=\frac{1}{6} \quad \mathrm{P}\left(\mathrm{E}{4}\right)=\frac{1}{6} \quad \mathrm{P}\left(\mathrm{E}{5}\right)=\frac{1}{6} \quad \mathrm{P}\left(\mathrm{E}{6}\right)=\frac{1}{6}$$
where $E_{i}$ defines the ith experimental outcome, i.e.
$E_{1}=1$ Observed value on the dice is a one
$E_{2}=2$ Observed value on the dice is a two
$E_{3}=3$ Observed value on the dice is a three
$E_{4}=4$ Observed value on the dice is a four
$E_{5}=5 \quad$ Observed value on the dice is a five
$E_{6}=6$ Observed value on the dice is a six
Again, note that the probability of the set of possible experimental outcomes equals one since
\begin{aligned} &\mathrm{P}\left(\mathrm{E}{1}\right)+\mathrm{P}\left(\mathrm{E}{2}\right)+\mathrm{P}\left(\mathrm{E}{3}\right)+\mathrm{P}\left(\mathrm{E}{4}\right)+\mathrm{P}\left(\mathrm{E}{5}\right)+\mathrm{P}\left(\mathrm{E}{6}\right) \ &=\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{6}{6}=1 . \end{aligned}

## 统计代写|非参数统计代写Nonparametric Statistics代考|RANDOM VARIABLES AND THEIR DISTRIBUTIONS

A random variable, denoted as $X$, can take on a value, or, an interval of values, with an associated probability. The random variable can be univariate (one) or bivariate (two) or even multivariate (more than two). There are two major types of random variables, namely, discrete and continuous. Although there are situations where there can be a mixed random variable, which is partly discrete and partly continuous, we focus on the discrete and continuous variables here. To illustrate a discrete random variable, let’s consider the coin example where either a head or a tail can be observed in a trial (a coin toss). Suppose that a coin is tossed five times and the random variable $X$ denotes the number of heads that are observed. Then $X$ can only take on integer values $\mathrm{S}={0,1,2,3,4,5}$ and, accordingly, $X$ is a discrete random variable. Another example of a discrete random variable would be an $X$ that denotes the number of members in a household. Alternatively, a continuous random variable can take on values within some range. The probability of a continuous variable taking on any specific value is zero. If $X$ denotes the height of a tree, then it is possible for a tree to have a height of $2.176 \mathrm{~m}$ or even $2.1765482895 \mathrm{~m}$; the number of decimal places depends on the accuracy of the measuring instrument. Thus $X$ can take on values other than only integer values, within some range of values and, accordingly, $X$ is a continuous random variable. Another example of a continuous random variable would be if $X$ denotes the lifetime of a light bulb.

## 统计代写|非参数统计代写NONPARAMETRIC STATISTICS代 考|BASIC PROBABILITY

$$\mathrm{P}(\mathrm{E} 1)=\frac{1}{6} \quad \mathrm{P}(\mathrm{E} 2)=\frac{1}{6} \quad \mathrm{P}(\mathrm{E} 3)=\frac{1}{6} \quad \mathrm{P}(\mathrm{E} 4)=\frac{1}{6} \quad \mathrm{P}(\mathrm{E} 5)=\frac{1}{6} \quad \mathrm{P}(\mathrm{E} 6)=\frac{1}{6}$$

## 统计代写|非参数统计代写NONPARAMETRIC STATISTICS代 考|RANDOM VARIABLES AND THEIR DISTRIBUTIONS

$\mathrm{S}=0,1,2,3,4,5$ 因此， $X$ 是离散随机变量。离散随机变量的另一个例子是 $X$ 表示一个家庭的成员人数。或者，连续随机变量可以取某个范围内的值。连续变量取 任何特定值的概率为零。如果 $X$ 表示一棵树的高度，那么一棵树的高度可能为 $2.176 \mathrm{~m}$ 甚至 $2.1765482895 \mathrm{~m}$; 小数位数取决于财量仪器的精度。因此 $X$ 可以在某些 值范围内采用除整数值以外的值，因此， $X$ 是一个连续随机变量。另一个连续随机变量的例子是如果 $X$ 表示灯泡的寿命。

## 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。