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HarvardX Data Science - Probability (PH125.3x)

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Updated 12/2024

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Course Description

Gain important foundational knowledge in probability theory, essential for data scientist, as you learn key concepts through a motivating case study on the financial crisis of 2007-08. Find the complete course on edx.org here.

Prerequisites

There are no prerequisites for this course

1

Introduction to Discrete Probability

Exercise 1. Probability of cyan - generalized

Exercise 2. Probability of not cyan - generalized

Exercise 3. Sampling without replacement - generalized

Exercise 4. Sampling with replacement - generalized

End of Assessment: Introduction to Discrete Probability

2

Independence and Multiplication Rule

Exercise 1. Independence

Exercise 2. Sampling with replacement

Exercise 3. Rolling a die

Exercise 4. Probability the Celtics win a game

Exercise 5. Monte Carlo simulation for Celtics winning a game

End of Assessment: Independence and Multiplication Rule

3

The Addition Rule

Exercise 1. The Cavs and the Warriors

Exercise 2. The Cavs and the Warriors - Monte Carlo

Exercise 3. A and B play a series - part 1

Exercise 4. A and B play a series - part 2

End of Assessment: The Addition Rule

4

Continuous Probability

Exercise 1. Distribution of female heights - 1

Exercise 2. Distribution of female heights - 2

Exercise 3. Distribution of female heights - 3

Exercise 4. Distribution of female heights - 4

Exercise 5. Probability of 1 SD from average

Exercise 6. Distribution of male heights

Exercise 7. Distribution of IQ scores

End of Assessment: Continuous Probability

5

Random Variables and Sampling Models

Exercise 1. American Roulette probabilities

Exercise 2. American Roulette payout

Exercise 3. American Roulette expected value

Exercise 4. American Roulette standard error

Exercise 5. American Roulette sum of winnings

Exercise 6. American Roulette winnings expected value

Exercise 7. American Roulette winnings expected value

End of Assessment: Random Variables and Sampling Models

6

The Central Limit Theorem

Exercise 1. American Roulette probability of winning money

Exercise 2. American Roulette Monte Carlo simulation

Exercise 3. American Roulette Monte Carlo vs CLT

Exercise 4. American Roulette Monte Carlo vs CLT comparison

Exercise 5. American Roulette average winnings per bet

Exercise 6. American Roulette per bet expected value

Exercise 7. American Roulette per bet standard error

Exercise 8. American Roulette winnings per game are positive

Exercise 9. American Roulette Monte Carlo again

Exercise 10. American Roulette comparison

Exercise 11. American Roulette comparison analysis

End of Assessment: The Central Limit Theorem

7

The Big Short

Exercise 1. Bank earnings

Exercise 2. Bank earnings Monte Carlo

Exercise 3. Bank earnings expected value

Exercise 4. Bank earnings standard error

Exercise 5. Bank earnings interest rate - 1

Exercise 6. Bank earnings interest rate - 2

Exercise 7. Bank earnings - minimize money loss

End of Assessment: The Big Short

HarvardX Data Science - Probability (PH125.3x)

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