## Probability

**Author(s):**

Jim Pitman

**Publisher:**

Springer

**Pages:**560

**Further Actions:**

**Categories:**

### AVAILABLE FORMATS

Hardcover - 9780387979748

03 June 1993

* $109.00*

**In stock**

Paperback - 9780387945941

01 April 1997

* $109.00*

**In stock**

Ebook - 9781461243748

06 December 2012

* $109.00*

**In stock**

This is a text for a one-quarter or one-semester course in probability, aimed at students who have done a year of calculus. The book is organised so a student can learn the fundamental ideas of probability from the first...

Show MoreThis is a text for a one-quarter or one-semester course in probability, aimed at students who have done a year of calculus. The book is organised so a student can learn the fundamental ideas of probability from the first three chapters without reliance on calculus. Later chapters develop these ideas further using calculus tools. The book contains more than the usual number of examples worked out in detail.

1.1 Equally Likely Outcomes

1.2 Interpretations

1.3 Distributions

1.4 Conditional Probability and Independence

1.5 Bayes’ Rule

1.6 Sequences of Events

Summary

Review Exercises

2 Repeated Trials and Sampling

2.1 The Binomial Distribution

2.2 Normal Approximation: Method

2.3 Normal Approximation: Derivation (Optional)

2.4 Poisson Approximation

2.5 Random Sampling

Summary

Review Exercises

3 Random Variables

3.1 Introduction

3.2 Expectation

3.3 Standard Deviation and Normal Approximation

3.4 Discrete Distributions

3.5 The Poisson Distribution

3.6 Symmetry (Optional)

Summary

Review Exercises

4 Continuous Distributions

4.1 Probability Densities

4.2 Exponential and Gamma Distributions

4.3 Hazard Rates (Optional)

4.4 Change of Variable

4.5 Cumulative Distribution Functions

4.6 Order Statistics (Optional)

Summary

Review Exercises

5 Continuous Joint Distributions

5.1 Uniform Distributions

5.2 Densities

5.3 Independent Normal Variables

5.4 Operations (Optional)

Summary

Review Exercises

6 Dependence

6.1 Conditional Distributions: Discrete Case

6.2 Conditional Expectation: Discrete Case

6.3 Conditioning: Density Case

6.4 Covariance and Correlation

6.5 Bivariate Normal

Summary

Review Exercises

Distribution Summaries

Discrete

Continuous

Beta

Binomial

Exponential

Gamma

Geometric and Negative Binomial

Hypergeometrie

Normal

Poisson

Uniform

Examinations

Solutions to Examinations

Appendices

1 Counting

2 Sums

3 Calculus

4 Exponents and Logarithms

5 Normal Table

Brief Solutions to Odd-Numbered Exercises.