18.05 Studio3 test answers

Problem 1a

This produces the following plot. Pay attention to the scale on the vertical axis.

studio3_problem_1a(1, 1000)

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## 1a. Frequency histogram

## See plot

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Problem 1b

This produces the following plot. Pay attention to the scale on the vertical axis.

studio3_problem_1b(1, 1000)

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## Problem 1b: Density histogram

## See plot

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Problem 2a

studio3_problem_2a(1, 1000)

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## Problem 2a: Density histogram

## See plot

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Problem 2b

This test runs studio3_problem_2b four times. Notice how as n_to_average increases, the average looks more and more like a normal distribution.

Each call produced a plot

studio3_problem_2b(1, 4000, 4, 0.05)

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## -----Problem 2b: Density histogram of average

## See plot

studio3_problem_2b(1, 4000, 8, 0.05)

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## -----Problem 2b: Density histogram of average

## See plot

studio3_problem_2b(1, 4000, 16, 0.05)

## 
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## -----Problem 2b: Density histogram of average

## See plot

studio3_problem_2b(1, 4000, 64, 0.05)

## 
## ----------------------------------
## -----Problem 2b: Density histogram of average

## See plot

Wow! We just illustrated the central limit theorem.

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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

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