Problem 0

studio6_problem_0()
## 
## ----------------------------------
## Problem 0: Averaging normal distributions

## 0. YOU NEED TO PUT YOUR COMPARISON OF THE HISTOGRAMS IN THE CAT STATEMENT.

Problem 1

Problem 1a

studio6_problem_1a()
## 
## ----------------------------------
## Problem 1a. Formula for Cauchy pdf
## 1a. YOU NEED TO PUT THE FORMULA f(x | theta) FOR THE CAUCHY DISTRIBUTION IN THE CAT STATEMENT.

Problem 1b

studio6_problem_1b()
## -----
## 1b. Plot pdf of Cauchy and standard normal

## 1b. See plots

Problem 1c

studio6_problem_1c()
## -----
## 1c. Explain fat tails
## 1c. YOU NEED TO PUT YOUR EXPLANATION FOR FAT TAILS IN THE CAT STATEMENT.

Problem 1d

studio6_problem_1d()
## -----
## 1d. Average of Cauchy distributions

## Notice that averaging the Cauchy distribution does not change the spread of the histogram. Averaging does not help us estimate the location of the pdf!

Problem 2

Problem 2a

studio6_problem_2a('mit18_05_s22_studio6_test_data_frame.csv')
## 
## ----------------------------------
## Problem 2a. Load and plot data.
##   X   position
## 1 1 -0.4912204
## 2 2 -7.2980783
## 3 3  0.4450264
## 4 4 -2.0139916
## 5 5 -3.3192671
## 6 6 -2.0919951

## 2a. See plot

Problem 2b

studio6_problem_2b('mit18_05_s22_studio6_test_data_frame.csv')
## -----
## 2b. Discretized Bayesian updates and MAP estimates.

## [1] "2b(iv) Final map estimate:  -0.94"

## 2b(vi). YOU NEED TO PUT YOUR CONCLUSION ON WHERE TO LOOK IN THE CAT STATEMENT.

Problem 2c (OPTIONAL)

studio6_problem_2c()
## -----
## Problem 2c (OPTIONAL). Explanation
## 2c (OPTIONAL). YOU NEED TO PUT YOUR EXPLANATION IN THE CAT STATEMENT.

MIT OpenCourseWare

https://ocw.mit.edu

18.05 Introduction to Probability and Statistics

Spring 2022

Authors: Jeremy Orloff and Jennifer French

For information about citing these materials or our Terms of Use, visit: https://ocw.mit.edu/terms