概率模型应用基础：Introduction to Probability Models 概览

3星 · 超过75%的资源需积分: 10 128 浏览量更新于2024-07-22 收藏 3.08MB PDF 举报

"《应用随机过程概率模型导论》是一本国际知名的介绍随机过程的教材，作者Sheldon M. Ross，来自南加州大学。该书以其简洁实用和易于理解的特点著称，适合初学者和专业人士学习。" 在《Introduction to Probability Models》第十版中，Sheldon M. Ross深入浅出地介绍了概率模型的基本概念和应用，特别是在随机过程领域的知识。随机过程是概率论的一个重要分支，广泛应用于自然科学、工程学、经济学等多个领域。书中的内容可能包括： 1. **随机过程基础**：首先，书中会介绍随机过程的基本定义，如离散时间与连续时间随机过程，以及它们的统计特性，如均值、方差、相关函数等。 2. **马尔科夫过程**（Markov Process）：这是随机过程中一个重要的概念，它描述了一个系统在未来的状态只依赖于当前状态，而不依赖于过去的历史。马尔科夫过程有广泛的应用，如物理学、化学、生物学、社会科学和计算机科学中的建模。 3. **隐马尔科夫模型**（Hidden Markov Model, HMM）：HMM是马尔科夫过程的一个扩展，其中观察到的序列是由隐藏的马尔科夫过程生成的。这种模型在语音识别、自然语言处理、生物信息学等领域有着重要应用。 4. **概率模型的构建与分析**：书中可能会详细讨论如何构建和分析各种类型的概率模型，包括泊松过程、布朗运动、Wiener过程（也称为布朗运动的一种特殊形式）和扩散过程等。 5. **应用案例**：为了帮助读者理解这些理论的实际应用，书中可能包含了大量的实际例子和问题，涵盖了工程、物理、经济等多个领域的应用。 6. **数学工具**：书中可能还会介绍一些用于处理随机过程的数学工具，如矩母函数、特征函数、生成函数等，以及如何利用这些工具进行概率分析。 7. **计算方法**：对于一些复杂模型，书中可能涉及数值方法和模拟技术，如蒙特卡洛模拟，以便于实际问题的求解。 8. **许可与版权信息**：书中明确指出未经许可，不得复制或以任何形式传播内容，但同时也指出了寻求许可的途径，如通过出版商的网站获取相关信息。《应用随机过程概率模型导论》是一本全面而深入的概率模型教科书，对于想要理解和应用随机过程的人来说，是一份宝贵的资源。通过阅读此书，读者可以系统性地学习并掌握随机过程理论及其在现实世界中的应用。

Preface xv

Jean Lemaire, University of Pennsylvania

Andrew Lim, University of California, Berkeley

George Michailidis, University of Michigan

Donald Minassian, Butler University

Joseph Mitchell, State University of New York, Stony Brook

Krzysztof Osfaszewski, University of Illinois

Erol Pekoz, Boston University

Evgeny Poletsky, Syracuse University

James Propp, University of Massachusetts, Lowell

Anthony Quas, University of Victoria

Charles H. Roumeliotis, Proofreader

David Scollnik, University of Calgary

Mary Shepherd, Northwest Missouri State University

Galen Shorack, University of Washington, Seattle

Marcus Sommereder, Vienna University of Technology

Osnat Stramer, University of Iowa

Gabor Szekeley, Bowling Green State University

Marlin Thomas, Purdue University

Henk Tijms, Vrije University

Zhenyuan Wang, University of Binghamton

Ward Whitt, Columbia University

Bo Xhang, Georgia University of Technology

Julie Zhou, University of Victoria

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)

剩余800页未读，继续阅读

yangyawen12312

粉丝: 0
资源: 2

概率模型应用基础：Introduction to Probability Models 概览

应用随机过程概率模型导论 第11版

应用随机过程概率模型导论pdf

应用随机过程概率模型导论 第11版 pdf

应用随机过程概率模型导论 第11版pdf

应用随机过程导论 11版pdf

指数随机图模型导论 pdf下载

随机过程刘次华第四版第四章课后习题答案

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

机器人操作de数学导论

introduction to probability. 2nd ed.

最新资源

应用随机过程概率模型导论第11版

应用随机过程概率模型导论第11版 pdf

应用随机过程概率模型导论第11版pdf