Overview

This homework assignment is the first assignment designed to get you

familiar with the programming basics. Your objective is to perform a series

of simulated "dice rolls", perform a basic statistical analysis, and plot the

results. You must do this assignment in MATLAB, but keep in mind

that you should also use whatever programming language your group is using

for the research topic.

For extra credit: You may do this assignment

in both MATLAB and PYTHON languages

Before you begin the coding, write an introduction explaining what you anticipate the results will be$.$

What can you say about the probabilities of outcomes in each case:

What should the probabilities be for each of the faces $($numbers$)$ for the single die roll?

What should the probabilities be for each of the combinations of the sum of the two dice roll?

What can you say about the sample means for each case:

How do the sample means change as we increase the number of rolls?

What should the mean be for the single die roll?

What should the mean be for the sum of the two dice roll?

Having thought about the expected outcomes and put your predictions in the introduction, move on to writing the code.

You will first "roll" an individual dice $10$ and $1000$ times, calculating the

mean, standard deviation, histogram, CFD and PDF for each set.

Then, you will "roll" two dice, adding together their sums, $10$ and $1000$ times. Again, calculating

the mean, standard deviation, histogram, CFD and PDF for each set of rolls.

Requirements

To fulfill this project, you must successfully program a script that utilizes

several different functions and loops to simulate dice rolls and calculate

the statistics. Each function should have a practical name, be easy to read

and understand, and function. You should also comment appropriately

throughout the program such that someone else could understand what is

occurring.

Submission

You will submit the following to the Canvas assignment box:

A summary MS WORD document with introduction, tables of the statistical parameters, and

copies of the generated histograms

Your well$-$documented code source files. Make sure the main script is named properly.

Note that any submitted code needs to be able to be executed without

any errors. Any additional libraries need to be able to be installed using a

package manager like pip.

$*$The main script should be named in the following format:

h$[$#$]\_[$ASSIGNMENTNAME$]\_[$LAST NAME$].[$EXTENSION$],$ for example, h$3\_$dice$\_$roll$\_$weaver.

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Extra Credit

If you are willing to dig in a little bit more, this project has a couple of opportunities to earn extra credit points

at the discretion of the instructor. First, you may do this assignment in both Python and MATLAB. Being able to

work with multiple programming languages is an extremely useful skill. Python and MATLAB are also close

enough in syntax that the code should not have to change much between them.

Additionally, you may write up to three different operations with the dice rolling and provide the same output

for each. For $10$ points of extra credit each, you may write functions that subtract, multiply, and divide the rolls

of two dice for $10$ and $1000$ rolls. You will only be granted the extra credit points if the full output for each

operation is provided!

Psuedocode

For those that are new to programming, a suggested code layout is given below in psuedocode to guide you.

Function: Roll One Die

Argument: iterations

Initialize zeroes array of length iterations

For every iteration

Sample a random integer from $[1,6]$

Add sample to array

Returns: array of random samples, mean of array, stdev of array

Function: Roll Two Dice and Sum

Argument: iterations

Initialize zeroes array of length iterations

For every iteration

Sample two random integers from $[1,6]$ and add together

Add the summation to array

Returns: array of summed samples, mean of array, stdev of array

Calculate array, mean, and stdev for $10$ single rolls

Calculate array, mean, and stdev for $1000$ single rolls

Generate output table for single rolls and print

Create singular die roll figure with two subplots

Plot bar graph for $10$ die rolls

Plot bar graph for $1000$ die rolls

Show figure

Calculate array, mean, stdev for $10$ summed dice rolls

Calculate array, mean, stdev for $1000$ summed dice rolls

Generate output table for summed rolls and print

Create summed dice roll figure with two subplots

Plot bar graph for $10$ summed dice rolls

Plot bar graph for $1000$ summed dice rolls

Show figure