## Introduction to Probability

By Grinstead and Snell.
Book is available in the
following link

These are my proposed solutions. If you find any mistakes, please let me know.

A lot of simulation exercises. These were done in R.

Skipping chapters 10 and out. Only interesting topic is Markov chains, but there are better books for that.

#### Chapter 1 - Discrete Probability Distributions

1.1 Simulation of Discrete Probabilities

1.2 Discrete Probability Distributions

#### Chapter 2 - Continuous Probability Densities

2.1 Simulation of Continuous Probabilities

2.2 Continuous Density Functions

#### Chapter 3 - Combinatorics

3.1 Permutations

3.2 Combinations

3.3 *[Skipped]* Card Shuffling

#### Chapter 4 - Conditional Probability

4.1 Discrete Conditional Probability

4.2 Continuous Conditional Probability

4.3 *[Skipped]* Paradoxes

#### Chapter 5 - Distributions and Densities

5.1 Important Distributions

5.2 Important Densities

#### Chapter 6 - Expected Value and Variance

6.1 Expected Value

6.2 Variance of Discrete Random Variables

6.3 Continuous Random Variables

#### Chapter 7 - Sums of Random Variables

7.1 Sums of Discrete Random Variables

7.2 Sums of Continuous Random Variables

#### Chapter 8 - Law of Large Numbers

8.1 Discrete Random Variables

8.2 Continuous Random Variables

#### Chapter 9 - Central Limit Theorem

9.1 Bernoulli Trials

9.2 Discrete Independent Trials

9.3 Continuous Independent Trials

#### Chapter 10 - Generating Functions

10.1 *[Skipped]* Discrete Distributions

10.2 *[Skipped]* Branching Processes

10.3 *[Skipped]* Continuous Densities

#### Chapter 11 - Markov Chains

11.1 *[Skipped]* Introduction

11.2 *[Skipped]* Absorbing Markov Chains

11.3 *[Skipped]* Ergodic Markov Chains

11.4 *[Skipped]* Fundamental Limit Theorem

11.5 *[Skipped]* Mean First Passage Time

#### Chapter 12 - Random Walks

12.1 *[Skipped]* Random Walks in Euclidean Space

12.2 *[Skipped]* Gamblerâ€™s Ruin

12.3 *[Skipped]* Arc Sine Laws