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# HarvardX Data Science - Probability (PH125.3x)

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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.

- 1
### Introduction to Discrete Probability

**Free**In this chapter, you will learn about the fundamentals of discrete probability through looking at examples of sampling from an urn with and without replacement.

- 2
### Independence and Multiplication Rule

**Free**In this chapter, you will learn about independence, conditional probability, and the multiplication rule through examples involving draws from an urn, rolls of a die, and sports series wins.

- 3
### The Addition Rule

**Free**In this chapter, you will learn about the addition rule and the Monty Hall problem.

- 4
### Continuous Probability

**Free**In this chapter, you will learn about continuous probability through the use of examples involving the distribution of heights and IQ scores.

Exercise 1. Distribution of female heights - 1100 xpExercise 2. Distribution of female heights - 2100 xpExercise 3. Distribution of female heights - 3100 xpExercise 4. Distribution of female heights - 4100 xpExercise 5. Probability of 1 SD from average100 xpExercise 6. Distribution of male heights100 xpExercise 7. Distribution of IQ scores100 xpEnd of Assessment: Continuous Probability50 xp - 5
### Random Variables and Sampling Models

**Free**In this chapter, you will learn about random variables and sampling models exploring an example looking at various aspects of the game of chance American Roulette.

Exercise 1. American Roulette probabilities100 xpExercise 2. American Roulette payout100 xpExercise 3. American Roulette expected value100 xpExercise 4. American Roulette standard error100 xpExercise 5. American Roulette sum of winnings100 xpExercise 6. American Roulette winnings expected value100 xpExercise 7. American Roulette winnings expected value100 xpEnd of Assessment: Random Variables and Sampling Models50 xp - 6
### The Central Limit Theorem

**Free**In this chapter, you will learn about the Central Limit Theorem and compare results from Monte Carlo simulations to those obtained using the Central Limit Theorem for games of chance.

Exercise 1. American Roulette probability of winning money100 xpExercise 2. American Roulette Monte Carlo simulation100 xpExercise 3. American Roulette Monte Carlo vs CLT100 xpExercise 4. American Roulette Monte Carlo vs CLT comparison50 xpExercise 5. American Roulette average winnings per bet100 xpExercise 6. American Roulette per bet expected value100 xpExercise 7. American Roulette per bet standard error100 xpExercise 8. American Roulette winnings per game are positive100 xpExercise 9. American Roulette Monte Carlo again100 xpExercise 10. American Roulette comparison100 xpExercise 11. American Roulette comparison analysis50 xpEnd of Assessment: The Central Limit Theorem50 xp - 7
### The Big Short

**Free**In this chapter, you will learn about interest rates and the big short.

Exercise 1. Bank earnings100 xpExercise 2. Bank earnings Monte Carlo100 xpExercise 3. Bank earnings expected value100 xpExercise 4. Bank earnings standard error100 xpExercise 5. Bank earnings interest rate - 1100 xpExercise 6. Bank earnings interest rate - 2100 xpExercise 7. Bank earnings - minimize money loss50 xpEnd of Assessment: The Big Short50 xp

#### Weston Stearns

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