罗斯第十版《概率模型入门》英文完整版798页详解

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《概率模型入门》第十版是由著名作者Sheldon M. Ross撰写的一本权威教材。该书针对初学者和专业人士提供了全面的概率论知识，是该领域的重要参考文献。全书共798页，详细介绍了概率论的基本概念、理论和应用，旨在帮助读者理解和掌握概率模型在各个领域的应用，如统计学、金融工程、机器学习等。该版本是英文版，适合那些希望深入理解英文原版理论和讨论的读者。Ross以其清晰的阐述风格和丰富的实例来解释复杂的概率概念，使抽象的理论易于理解。书中涵盖的内容包括但不限于： 1. **概率基础**：从概率空间、随机变量、事件的定义和性质开始，讲解概率的加法原理、乘法规则以及条件概率。 2. **离散随机变量**：涉及伯努利试验、二项分布、几何分布、泊松分布等，以及随机变量的期望值和方差。 3. **连续随机变量**：包括正态分布、均匀分布、指数分布等，以及概率密度函数和累积分布函数的计算。 4. **随机变量的独立性和相关性**：研究随机变量之间的关系及其对总体概率的影响。 5. **随机过程**：介绍随机序列和随机字段的概念，探讨它们在通信、信号处理中的应用。 6. **极限定理**：如大数定律和中心极限定理，这些对于理解数据集中趋势和变异性至关重要。 7. **概率模型的应用**：包括决策理论、风险分析、金融衍生品定价等领域中的概率模型实例。 8. **蒙特卡洛方法**：一种基于随机抽样解决问题的方法，广泛应用于模拟和优化。此外，版权方面，本书受Elsevier出版集团保护，未经许可不得复制或传播任何形式的内容，读者需通过Elsevier官网获取正式授权。书中还包含了关于版权许可政策的信息，以确保遵循国际版权法规。《概率模型入门》第十版是一本深度与实用性兼备的教材，不仅适合大学概率论课程的学习者，也是专业人员提升技能、扩展知识库的宝贵资源。通过深入阅读和实践书中的内容，读者将能够建立起扎实的概率论基础，为后续在相关领域的工作和研究打下坚实的基础。

2 Introduction to Probability Theory

Some examples are the following.

1. If the experiment consists of the ﬂipping of a coin, then

S ={H, T}

where H means that the outcome of the toss is a head and T that it is a tail.

2. If the experiment consists of rolling a die, then the sample space is

S ={1, 2, 3, 4, 5, 6}

where the outcome i means that i appeared on the die, i = 1, 2, 3, 4, 5, 6.

3. If the experiments consists of ﬂipping two coins, then the sample space consists of the

following four points:

S ={(H, H), (H, T), (T, H), (T, T)}

The outcome will be (H, H) if both coins come up heads; it will be (H, T) if the

ﬁrst coin comes up heads and the second comes up tails; it will be (T, H) if the

ﬁrst comes up tails and the second heads; and it will be (T, T) if both coins come

up tails.

4. If the experiment consists of rolling two dice, then the sample space consists of the

following 36 points:

S =

⎧

⎪

⎨

⎪

⎩

(1, 1), (1, 2), (1, 3), (1,

4), (1,

5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,

(6,

1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

⎫

⎪

⎬

⎪

⎭

where the outcome (i, j ) is said to occur if i appears on the ﬁrst die and j on the second

die.

5. If the experiment consists of measuring the lifetime of a car, then the sample space

consists of all nonnegative real numbers. That is,

S =[0, ∞)

∗



Any subset E of the sample space S is known as an event. Some examples of

events are the following.



. In Example (1), if E ={H}, then E is the event that a head appears on the ﬂip of the

coin. Similarly, if E ={T}, then E would be the event that a tail appears.



. In Example (2), if E ={1}, then E is the event that one appears on the roll of the

die. If E ={2, 4, 6}, then E would be the event that an even number appears on

the roll.

∗

The set (a, b) is deﬁned to consist of all points x such that a < x < b. The set [a, b] is deﬁned

to consist of all points x such that a  x  b. The sets (a, b] and [a, b) are deﬁned, respectively, to

consist of all points x such that a < x  b and all points x such that a  x < b.

1.2 Sample Space and Events 3



. In Example (3), if E ={(H, H), (H, T)}, then E is the event that a head appears on

the ﬁrst coin.



. In Example (4), if E ={(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}, then E is the event

that the sum of the dice equals seven.



. In Example (5), if E = (2, 6), then E is the event that the car lasts between two and six

years. 

We say that the event E occurs when the outcome of the experiment lies in E.

For any two events E and F of a sample space S we deﬁne the new event E ∪ F

to consist of all outcomes that are either in E or in F or in both E and F. That is,

the event E ∪ F will occur if either E or F occurs. For example, in (1) if E ={H}

and F ={T}, then

E ∪ F ={H, T}

That is, E ∪ F would be the whole sample space S. In (2) if E ={1, 3, 5} and

F ={1, 2, 3}, then

E ∪ F ={1, 2, 3, 5}

and thus E ∪ F would occur if the outcome of the die is 1 or 2 or 3 or 5. The

event E ∪ F is often referred to as the union of the event E and the event F.

For any two events E and F, we may also deﬁne the new event EF, sometimes

written E ∩F, and referred to as the intersection of E and F,

follows. EF consists

of all outcomes which are both in E and in F. That is, the event EF will occur

only if both E and F occur. For example, in (2) if E ={1, 3, 5} and F ={1, 2, 3},

then

EF ={1, 3}

and thus EF would occur if the outcome of the die is either 1 or 3. In Exam-

ple (1) if E ={H} and F ={T}, then the event EF would not consist of any

outcomes and hence could not occur. To give such an event a name, we shall

refer to it as the null event and denote it by Ø. (That is, Ø refers to the event

consisting of no outcomes.) If EF = Ø, then E and F are said to be mutually

exclusive.

We also deﬁne unions and intersections of more than two events in a simi-

lar manner. If E

, E

, ... are events, then the union of these events, denoted by



∞

n=1

, is deﬁned to be the event that consists of all outcomes that are in E

for at least one value of n = 1, 2, .... Similarly, the intersection of the events E

denoted by



∞

n=1

, is deﬁned to be the event consisting of those outcomes that

are in all of the events E

, n = 1, 2, ... .

Finally, for any event E we deﬁne the new event E

, referred to as the

complement of E, to consist of all outcomes in the sample space S that are not

in E. That is, E

will occur if and only if E does not occur. In Example (4)

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罗斯第十版《概率模型入门》英文完整版798页详解

随机过程(sheldon M.Ross著)

Introduction to Probability.pdf

(Prob) Ross, Introduction to Probability Models 10th.pdf

introduction to probability models, by sheldon m. ross, 10th edition, elsevi

Solutions of Introduction to probability models [10th]

Introduction to Probability Models 10th Edition

Introduction to Probability Models 11th

概率模型入门：Sheldon M. Ross的《Introduction to Probability Models》第九版解析

概率模型基础：Sheldon M. Ross的第9版解析

概率模型基础：Sheldon M. Ross的第九版简介

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