Probability

by Lawrence M Leemis

Overview

This calculus-based introduction to probability covers all of the traditional topics, along with a secondary emphasis on Monte Carlo simulation. Examples that introduce applications from a wide range of fields help the reader apply probability theory to real-world problems. The text covers all of the topics associated with Exam P given by the Society of Actuaries. Over 100 figures highlight the intuitive and geometric aspects of probability. Over 800 exercises are used to reinforce concepts and make this text appropriate for classroom use.

Product Details

ISBN-13:	9780982917473
Publisher:	Lawrence Leemis
Publication date:	10/06/2017
Edition description:	Second edition
Pages:	566
Product dimensions:	7.00(w) x 10.00(h) x 1.15(d)

Table of Contents

Probability

1. Introduction

1.1 Applications

1.2 Counting

1.3 Sets

2. Probability

2.1 Experiments, Sample Spaces, and Events

2.2 Probability Axioms

2.3 Computing Probabilities

2.4 Conditional Probability

2.5 Rule of Bayes

2.6 Independence

3. Random Variables

3.1 Discrete Random Variables

3.2 Continuous Random Variables

3.3 Cumulative Distribution Functions

3.4 Expected Values

3.5 Inequalities (Markov, Chebyshev)

4. Common Discrete Distributions

4.1 Bernoulli Distribution

4.2 Binomial Distribution

4.3 Geometric Distribution

4.4 Negative Binomial Distribution

4.5 Poisson Distribution

4.6 Hypergeometric Distribution

4.7 Other Distributions

5. Common Continuous Distributions

5.1 Uniform Distribution

5.2 Exponential Distribution

5.3 Gamma Distribution

5.4 Normal Distribution

5.5 Other Distributions

6. Joint Distributions

6.1 Bivariate Distributions

6.2 Independent Random Variables

6.3 Expected Values

6.4 Bivariate Normal Distribution

6.5 Multivariate Distributions

7. Functions of Random Variables

7.1 Cumulative Distribution Function Technique

7.2 Transformation Technique

7.3 Moment Generating Function Technique

8. Limit Theorems

8.1 Convergence in Probability

8.2 Convergence in Distribution

8.3 Central Limit Theorem