Basic Probability Theory

This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Its sole prerequisite is calculus.

**Tag(s):**
Probability

**Publication date**: 26 Jun 2008

**ISBN-10**:
0486466280

**ISBN-13**:
9780486466286

**Paperback**:
352 pages

**Views**: 1,753

Basic Probability Theory

This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Its sole prerequisite is calculus.

Book Description:

This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus.

Taking statistics as its major field of application, the text opens with a review of basic concepts, advancing to surveys of random variables, the properties of expectation, conditional probability and expectation, and characteristic functions. Subsequent topics include infinite sequences of random variables, Markov chains, and an introduction to statistics. Complete solutions to some of the problems appear at the end of the book.

This introduction to more advanced courses in probability and real analysis emphasizes the probabilistic way of thinking, rather than measure-theoretic concepts. Geared toward advanced undergraduates and graduate students, its sole prerequisite is calculus.

Taking statistics as its major field of application, the text opens with a review of basic concepts, advancing to surveys of random variables, the properties of expectation, conditional probability and expectation, and characteristic functions. Subsequent topics include infinite sequences of random variables, Markov chains, and an introduction to statistics. Complete solutions to some of the problems appear at the end of the book.

Tweet

About The Author(s)

Robert B. Ash (1935-2015) is Professor Emeritus of Mathematics in the Department of Mathematics at the University of Illinois. He was an Assistant Professor in Electrical Engineering at Columbia University and then a Visiting Assistant Professor at the University of California, Berkeley, before coming to the University of Illinois Department of Mathematics in 1963. He retired in 1990. Bob wrote thirteen textbooks but he was most proud of the eight books he posted on his web page during his retirement that were available for free downloading.

Book Categories

Computer Science
15
Introduction to Computer Science
32
Introduction to Computer Programming
52
Algorithms and Data Structures
24
Artificial Intelligence
24
Computer Vision
28
Machine Learning
6
Neural Networks
22
Game Development and Multimedia
25
Data Communication and Networks
5
Coding Theory
14
Computer Security
8
Information Security
34
Cryptography
3
Information Theory
17
Computer Organization and Architecture
22
Operating Systems
1
Image Processing
10
Parallel Computing
4
Concurrent Programming
20
Relational Database
3
Document-oriented Database
13
Data Mining
16
Big Data
17
Data Science
23
Digital Libraries
22
Compiler Design and Construction
26
Functional Programming
11
Logic Programming
26
Object Oriented Programming
21
Formal Methods
69
Software Engineering
3
Agile Software Development
7
Information Systems
5
Geographic Information System (GIS)

Mathematics
66
Mathematics
13
Algebra
1
Abstract Algebra
27
Linear Algebra
3
Number Theory
8
Numerical Methods
2
Precalculus
10
Calculus
1
Differential Equations
5
Category Theory
10
Proofs
19
Discrete Mathematics
24
Theory of Computation
14
Graph Theory
1
Complex Analysis
14
Probability
43
Statistics
7
Game Theory
5
Queueing Theory
13
Operations Research
16
Computer Aided Mathematics

Supporting Fields
19
Web Design and Development
1
Mobile App Design and Development
28
System Administration
2
Cloud Computing
9
Electric Circuits
6
Embedded System
26
Signal Processing
4
Network Science
3
Project Management

Operating System
Programming/Scripting
6
Ada
13
Assembly
34
C / C++
8
Common Lisp
2
Forth
35
Java
12
JavaScript
1
Lua
15
Microsoft .NET
1
Rexx
12
Perl
6
PHP
66
Python
12
R
1
Rebol
13
Ruby
2
Scheme
3
Tcl/Tk

Miscellaneous