## Solution Manual For First Course In Probability, A, 10th Edition

Solution Manual For First Course In Probability, A, 10th Edition

### 1. Combinatorial Analysis

- 1.1 Introduction
- 1.2 The Basic Principle of Counting
- 1.3 Permutations
- 1.4 Combinations
- 1.5 Multinomial Coefficients
- 1.6 The Number of Integer Solutions of Equations
- Summary
- Problems
- Theoretical Exercises
- Self-Test Problems and Exercises

### 2. Axioms of Probability

- 2.1 Introduction
- 2.2 Sample Space and Events
- 2.3 Axioms of Probability
- 2.4 Some Simple Propositions
- 2.5 Sample Spaces Having Equally Likely Outcomes
- 2.6 Probability as a Continuous Set Function
- 2.7 Probability as a Measure of Belief
- Summary
- Problems
- Theoretical Exercises
- Self-Test Problems and Exercises

### 3. Conditional Probability and Inference

- 3.1 Introduction
- 3.2 Conditional Probabilities
- 3.3 Bayes’s Formula
- 3.4 Independent Events
- 3.5
*P*(·|*F*) Is a Probability - Summary
- Problems
- Theoretical Exercises
- Self-Test Problems and Exercises

### 4. Random Variables

- 4.1 Random Variables
- 4.2 Discrete Random Variables
- 4.3 Expected Value
- 4.4 Expectation of a Function of a Random Variable
- 4.5 Variance
- 4.6 The Bernoulli and Binomial Random Variables
- 4.7 The Poisson Random Variable
- 4.8 Other Discrete Probability Distributions
- 4.9 Expected Value of Sums of Random Variables
- 4.10 Properties of the Cumulative Distribution Function
- Summary
- Problems
- Theoretical Exercises
- Self-Test Problems and Exercises

### 5. Continuous Random Variables

- 5.1 Introduction
- 5.2 Expectation and Variance of Continuous Random Variables
- 5.3 The Uniform Random Variable
- 5.4 Normal Random Variables
- 5.5 Exponential Random Variables
- 5.6 Other Continuous Distributions
- 5.7 The Distribution of a Function of a Random Variable
- Summary
- Problems
- Theoretical Exercises
- Self-Test Problems and Exercises

### 6. Jointly Distributed Random Variables

- 6.1 Joint Distribution Functions
- 6.2 Independent Random Variables
- 6.3 Sums of Independent Random Variables
- 6.4 Conditional Distributions: Discrete Case
- 6.5 Conditional Distributions: Continuous Case
- 6.6 Order Statistics
- 6.7 Joint Probability Distribution of Functions of Random Variables
- 6.8 Exchangeable Random Variables
- Summary
- Problems
- Theoretical Exercises
- Self-Test Problems and Exercises

### 7. Properties of Expectation

- 7.1 Introduction
- 7.2 Expectation of Sums of Random Variables
- 7.3 Moments of the Number of Events that Occur
- 7.4 Covariance, Variance of Sums, and Correlations
- 7.5 Conditional Expectation
- 7.6 Conditional Expectation and Prediction
- 7.7 Moment Generating Functions
- 7.8 Additional Properties of Normal Random Variables
- 7.9 General Definition of Expectation
- Summary
- Problems
- Theoretical Exercises
- Self-Test Problems and Exercises

### 8. Limit Theorems

- 8.1 Introduction
- 8.2 Chebyshev’s Inequality and the Weak Law of Large Numbers
- 8.3 The Central Limit Theorem
- 8.4 The Strong Law of Large Numbers
- 8.5 Other Inequalities and a Poisson Limit Result
- 8.6 Bounding the Error Probability When Approximating a Sum of Independent Bernoulli Random Variables by a Poisson Random Variable
- 8.7 The Lorenz Curve
- Summary
- Problems
- Theoretical Exercises
- Self-Test Problems and Exercises

### 9. Additional Topics in Probability

- 9.1 The Poisson Process
- 9.2 Markov Chains
- 9.3 Surprise, Uncertainty, and Entropy
- 9.4 Coding Theory and Entropy
- Summary
- Problems and Theoretical Exercises
- Self-Test Problems and Exercises

### 10. Simulation

- 10.1 Introduction
- 10.2 General Techniques for Simulating Continuous Random Variables
- 10.3 Simulating from Discrete Distributions
- 10.4 Variance Reduction Techniques
- Summary
- Problems
- Self-Test Problems and Exercises

#### Answers to Selected Problems

#### Solutions to Self-Test Problems and Exercises

#### Index

#### Common Discrete Distributions

#### Common Continuous Distributions

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