Problem 1

Problem 1a

studio4_problem_1a(10, 8, 10000)
## 
## ----------------------------------
## Problem 1a. Barto and Axel simulated covariance and correlation.
## For n_together = 10  and n_Barto_alone = 8 we have
## Axel's sample mean is -0.4906 
## Barto's sample mean is -0.8646 
## Axel's sample variance is 9.951107 
## Barto's sample variance is 17.94906 
## Their sample covariance is 9.949222 
## Their sample correlation is 0.7444449

Problem 1b

This problem asks for a description of what happens to the covariance and correlation as the number of bets Barho makes alone increases.

studio4_problem_1b()
## -----
## 1b. Describe behavior as n_Barto_alone increases
## As n_Barto_alone increases the covariance, YOUR_DESCRIPTION_HERE. 
## As n_Barto_alone increases the correlation, YOUR_DESCRIPTION_HERE.

Problem 2

This produces the following plot.

studio4_problem_2(800, 10000)
## 
## ----------------------------------
## Problem 2. Simulated central limit theorem.

## See plot

Wow! We just illustrated the central limit theorem.

MIT OpenCourseWare

https://ocw.mit.edu

18.05 Introduction to Probability and Statistics

Spring 2022

Authors: Jeremy Orloff and Jennifer French

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