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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|Conditional probability and independence

We start with the by-now-familiar setup of an experiment, a probability space $(\Omega, \mathcal{F}, \mathrm{P})$, and an event of interest $A$. The probability $\mathrm{P}(A)$ gives us an indication of how likely it is that the outcome of the experiment, $\omega \in \Omega$, is in $A$, that is, how likely the event $A$ is to occur. Now suppose that we know that event $B$ has occurred. This will alter our perception of how probable $A$ is since we are now only interested in outcomes that are in $B$. In effect we have shrunk the sample space from $\Omega$ to $B$. In these circumstances the appropriate measure is given by conditional probability.
Definition 2.4.1 (Conditional probability)
Consider the probability space $(\Omega, \mathcal{F}, \mathrm{P})$ and $A, B \in \mathcal{F}$ with $\mathrm{P}(B)>0$. The conditional probability of $A$ given $B$ is the probability that $A$ will occur given that $B$ has occurred,
$$\mathrm{P}(A \mid B)=\frac{\mathrm{P}(A \cap B)}{\mathrm{P}(B)} .$$
Note the importance of the statement that $\mathrm{P}(B)>0$. We cannot condition on events with zero probability. This makes sense intuitively; it is only reasonable to condition on events that have some chance of happening. The following example illustrates the use of Definition 2.4.1.
Example 2.4.2 (Rolling two dice again) Consider the setup in Example 2.1.1. We have shown that, if we roll two fair dice and $A$ is the event that the sum of the two values is greater than 10 , then $\mathrm{P}(A)=\frac{1}{12}$. Now suppose that event $B$ is the event that the value on the second die is a 6 . The situation is illustrated in Figure 2.2. By looking at the sample space, we can see that $|B|=6$ and $|A \cap B|=2$, so $\mathrm{P}(B)=\frac{1}{6}$ and $\mathrm{P}(A \cap B)=\frac{1}{18}$. By Definition 2.4.1, $\mathrm{P}(A \mid B)=\frac{1}{18} / \frac{1}{6}=\frac{1}{3}$.

统计代写|统计推断代写Statistical inference代考|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)
Define a random variable $X$ to be the number of heads when we flip a coin three times. We assume that flips are independent and that the probability of a head at each flip is $p$. We know that $X$ can take one of four values, $0,1,2$, or 3 . For convenience,we say that $X$ can take any real value, but the probability of it taking a value outside ${0,1,2,3}$ is zero. The probabilities evaluated in Example $2.4 .14$ can now be written as
$$\mathrm{P}(X=x)= \begin{cases}(1-p)^3, & x=0 \ 3 p(1-p)^2, & x=1 \ 3 p^2(1-p), & x=2 \ p^3, & x=3 \ 0, & \text { otherwise. }\end{cases}$$
The final line in this statement is often omitted; it is assumed that we have zero probability for values not explicitly mentioned. We can write down an equivalent formulation in terms of probability below a point:
$$\mathrm{P}(X \leq x)=\left{\begin{array}{lr} 0, & -\infty<x<0 \ (1-p)^3, & 0 \leq x<1 \ (1-p)^2(1+2 p), & 1 \leq x<2 \ 1-p^3, & 2 \leq x<3 \ 1, & 3 \leq x<\infty \end{array}\right.$$

统计推断代考

统计代写|统计推断代写统计推断代考|条件概率和独立性

.

$$\mathrm{P}(A \mid B)=\frac{\mathrm{P}(A \cap B)}{\mathrm{P}(B)} .$$

统计代写|统计推断代写统计推断代考|将结果映射到实数

.

$$\mathrm{P}(X=x)= \begin{cases}(1-p)^3, & x=0 \ 3 p(1-p)^2, & x=1 \ 3 p^2(1-p), & x=2 \ p^3, & x=3 \ 0, & \text { otherwise. }\end{cases}$$
。假设没有明确提到的值的概率为零。我们可以用低于某点的概率写出一个等价的公式:
$$\mathrm{P}(X \leq x)=\left{\begin{array}{lr} 0, & -\infty<x<0 \ (1-p)^3, & 0 \leq x<1 \ (1-p)^2(1+2 p), & 1 \leq x<2 \ 1-p^3, & 2 \leq x<3 \ 1, & 3 \leq x<\infty \end{array}\right.$$

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