Math 3339 – Fall 2024
Homework 1 (Chapter 1 & Chapter 3)
Name:__________________________________ PeopleSoft ID:_______________
Instructions:
Homework will NOT be accepted through email or in person. Homework must be submitted through
CANVAS BEFORE the deadline.
Total possible points: 100
a
1. This exercise relates to the College data set, which can be found in the file College.csv. It contains a
number of variables for 777 different universities and colleges in the US. Identify the types of the
following variables.
Private: Public/private indicator
F.Undergrade: Number of full-time undergraduates
S.F.Ratio: Student/faculty ratio
b
2. Suppose a family contains two children of different ages, and we are interested in the gender of these
children. Let F denote that a child is female and M that the child is male and let a pair such as FM
denote that the older child is female and the younger is male. There are four points in the set S of
possible observations:
S = {FF, FM, MF, MM}
Let A denote the subset of possibilities containing no males; B, the subset containing two males; and
C, the subset containing at least one male. List the elements of A, B, C, A∩B, A ∪ B, A∩C, A ∪ C,
B∩C, B ∪ C, and C∩ 𝐵.
a
An Introduction to Statistical Learning, James, G. et al (2013), Chapter 2
b
Mathematical Statistics with applications, Wackerly, D. et al (2011), Chapter 2
, 3. The “Boston” data set is a built-in dataset in the “MASS” library of R. The “Boston” data set contains
information about the housing values in suburbs of Boston city. First, load the “Boston” data set into
your R workspace. In Rstudio, you can click on the “Packages” tab and then on the checkbox next to
MASS. Without Rstudio, type the following command in R console:
data(Boston,package=”MASS”)
To know more information about this dataset, type the following command in R console:
?Boston
Then, answer the following questions based on the dataset, using R/Rstudio:
a. How many rows and columns in this data set?
b. How many of the suburbs in this dataset bound the Charles River? (Hint: Variable chas is a
dummy variable; chas=1 means tract bounds river, 0 otherwise) You can obtain a list of suburbs
bound the Charles River with the command:
subset(Boston,chas==1)
You can obtain a count of the suburbs bound the Charles River by
sum(Boston$chas==1)
c. What is the probability that you randomly select a suburb that bounds the Charles River?
a
An Introduction to Statistical Learning, James, G. et al (2013), Chapter 2
b
Mathematical Statistics with applications, Wackerly, D. et al (2011), Chapter 2
Homework 1 (Chapter 1 & Chapter 3)
Name:__________________________________ PeopleSoft ID:_______________
Instructions:
Homework will NOT be accepted through email or in person. Homework must be submitted through
CANVAS BEFORE the deadline.
Total possible points: 100
a
1. This exercise relates to the College data set, which can be found in the file College.csv. It contains a
number of variables for 777 different universities and colleges in the US. Identify the types of the
following variables.
Private: Public/private indicator
F.Undergrade: Number of full-time undergraduates
S.F.Ratio: Student/faculty ratio
b
2. Suppose a family contains two children of different ages, and we are interested in the gender of these
children. Let F denote that a child is female and M that the child is male and let a pair such as FM
denote that the older child is female and the younger is male. There are four points in the set S of
possible observations:
S = {FF, FM, MF, MM}
Let A denote the subset of possibilities containing no males; B, the subset containing two males; and
C, the subset containing at least one male. List the elements of A, B, C, A∩B, A ∪ B, A∩C, A ∪ C,
B∩C, B ∪ C, and C∩ 𝐵.
a
An Introduction to Statistical Learning, James, G. et al (2013), Chapter 2
b
Mathematical Statistics with applications, Wackerly, D. et al (2011), Chapter 2
, 3. The “Boston” data set is a built-in dataset in the “MASS” library of R. The “Boston” data set contains
information about the housing values in suburbs of Boston city. First, load the “Boston” data set into
your R workspace. In Rstudio, you can click on the “Packages” tab and then on the checkbox next to
MASS. Without Rstudio, type the following command in R console:
data(Boston,package=”MASS”)
To know more information about this dataset, type the following command in R console:
?Boston
Then, answer the following questions based on the dataset, using R/Rstudio:
a. How many rows and columns in this data set?
b. How many of the suburbs in this dataset bound the Charles River? (Hint: Variable chas is a
dummy variable; chas=1 means tract bounds river, 0 otherwise) You can obtain a list of suburbs
bound the Charles River with the command:
subset(Boston,chas==1)
You can obtain a count of the suburbs bound the Charles River by
sum(Boston$chas==1)
c. What is the probability that you randomly select a suburb that bounds the Charles River?
a
An Introduction to Statistical Learning, James, G. et al (2013), Chapter 2
b
Mathematical Statistics with applications, Wackerly, D. et al (2011), Chapter 2
