# Week 5 – Probability

## Lecture (February 7th) 👨🏫

## Readings 📖

- Fermat and Pascal on Probability: skim, but read
- Wikipedia, Lady tasting tea
- Stahl, The Evolution of the Normal Distribution, Pages 105-106
- YouTube: Normal distribution’s probability density function derived in 5min
- Rosenfeld, History of Probability (Part 3) - Jacob Bernoulli (1654-1705) – Law of Large Numbers

Optional:

- Sheynin, Theory of Probability. A Historical Essay: very detailed, but contains lots of interesting tidbits
- YouTube: Can You Solve The Problem That Inspired Probability Theory?: another explanation of the Problem of Points
- Cherowitzo, The Problem of Points slides
- YouTube: This DERIVATION of the BELL CURVE will SHOCK you!!!: another, much longer derivation of the normal distribution
- YouTube: Integral of exp(-x^2): watch if you want to see a proof that \(\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}\), using techniques from Math 20C

## Homework 5 (due Sunday, February 13th at 11:59PM) (solutions) 📝

Submit your answers as a PDF to Gradescope by the due date for full credit. We encourage you to discuss the readings and questions with others in the course, but all work must be your own. **Remember to use Campuswire if you need guidance!**

### Question 1

In class, we focused on development of the field of probability by Gauss, Fermat, Pascal, and Fisher. However, there were several other contributors to the field of probability. One prominent contributor was Jakob Bernoulli, whose name may sound familiar if you’ve heard of the Bernoulli probability distribution before in other contexts.

Read History of Probability (Part 3) - Jacob Bernoulli (1654-1705) – Law of Large Numbers. Then, answer the following questions:

- In your words, what is the law of large numbers?
- How did we use the law of large numbers in DSC 10, and how did we use it in Lecture 5?

### Question 2

This question is contained with a Jupyter Notebook, which is linked here. All of your answers (including screenshots of your code) should end up in your submitted PDF; you will not be submitting this notebook anywhere.

### (Optional / Make Up) Question 3

**Note:** This question is optional, though if you’ve missed a lecture or didn’t receive full credit on an earlier assignment, you can “make up” **one** of those things by completing this question.

This question can be found in the same Jupyter Notebook as Question 2, linked above.