Homework Zero Sample Assignment
Due: 12:00 pm (noon) on a Tuesday
In Canvas, you will see two assignments pages corresponding to Homework 1: (1) to
... [Show More] upload your write-up
PDF file and (2) to upload the R script that you used to generate your write-up. Your write-up is what will
be graded. The R script will not be graded, but you must submit it to receive credit on the write-up.
For all probability derivations, make sure to show your work and/or explain your reasoning. Do not include
your raw R code in your write-up unless we explicitly ask for it. You will submit your R script as
a separate document to the write-up itself.
Problem 1 – The Ludic Fallacy?
We throw two dice. Each one is a normal die with six equally-weighted sides. What is the probability that
the sum of the two numbers is less than 7?
Problem 2 – “The Iron Bank will have its due”
At the Iron Bank, 62% of customers have checking accounts, 24% have savings accounts, and 17% have both
checking and savings accounts.
Part A Of the Iron Bank customers who hold checking accounts, what percentage also have a savings
account?
Part B What is the probability that an Iron Bank customer has neither a checking account nor a savings
account?
Part C What proportion of Iron Bank customers have a savings account but not a checking account?
Problem 3 – Top Gun
If an aircraft is present in a certain area, a radar correctly registers its presence with probability 0.99. If it is
not present, the radar falsely registers an aircraft presence with probability 0.10. Suppose that on average
across all days, an aircraft is present with probability 0.05.
The radar today just registered the presence of an aircraft. What is the probability that an aircraft is actually
present? Make sure to show your work.
Problem 4 – “Picture me rollin”’
Download the s550.csv data set from the course Canvas site. This file contains a sample of 1501 Mercedes
S-Class S550 cars offered for sale in the U.S. via cars.com. There are several variables in the data set, but for
this problem the three relevant ones are mileage, price, and year.
Using the ggplot function within the ggplot2 R library, make a scatterplot of price (y) versus mileage (x),
faceted by year. (That is, there should be a separate panel for each year.) Format your figure so that it has 2
rows of 4 panels each, so that it looks wider than it is tall.
All you need to include in your write-up for this problem is the figure itself. To copy and paste from RStudio
directly into a Word file or Google doc, click the Zoom button in RStudio under the plots tab. This should
give you a resizeable window that you can copy/paste directly from. Pick an aspect ratio for the figure that
looks good in your write-up.
Problem 5 – CAPM
An important model that finance professionals use to understand asset prices is called the Capital Asset
Pricing Model (CAPM). You will learn more about the CAPM in a future finance course. But the basic
assumption of the model is that the rate of return on an individual stock is linearly related to the rate of
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