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first homework assignment, Exercises of Mathematics

Mathematics

Homework 1 MAth statistics fall 2023

Typology: Exercises

2022/2023

Uploaded on 12/04/2023

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mary432 🇺🇸

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bg1
a An Introduction to Statistical Learning, James, G. et al (2013), Chapter 2
b Mathematical Statistics, Wackerly, D. et al (2011), Chapter 2
Math 3339
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
1. aThis 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
2. bA group of five applications for a pair of identical jobs consists of three men and two women. The
employer is to select two of the five applicants for the jobs. Let S denote the set of all possible
outcomes for the employer’s selection. Let A denote the subset of outcomes corresponding to the
selection of two men and B the subset corresponding to the selection of at least one woman. List the
outcomes in A, 𝐵
, A∩B, A ∪ B, and A∩ 𝐵
. (Denote the different men and women by M1, M2, M3, and
W1, W2, respectively.)
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Download first homework assignment and more Exercises Mathematics in PDF only on Docsity!

a (^) An Introduction to Statistical Learning, James, G. et al (2013), Chapter 2

Math 3339

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
  1. aThis 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
  2. bA group of five applications for a pair of identical jobs consists of three men and two women. The employer is to select two of the five applicants for the jobs. Let S denote the set of all possible outcomes for the employer’s selection. Let A denote the subset of outcomes corresponding to the selection of two men and B the subset corresponding to the selection of at least one woman. List the outcomes in A , 𝐵̅ , A ∩ B , A ∪ B , and A ∩ 𝐵̅. (Denote the different men and women by M 1 , M 2 , M 3 , and W 1 , W 2 , respectively.)

-> Categorical (nominal)

-> Quantitative (Discrete -> (^) Quantitative /Continuous · (^) APP, Accept (^) , Enroll, toplo,Top (^25) , Undergrad ,^ outstate,^ Room/Board

S

Quantitative (Discrete

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a (^) An Introduction to Statistical Learning, James, G. et al (2013), Chapter 2

  1. Answer the following questions: a. A hand of 5 - card draw poker is a simple random sample from the standard deck of 52 cards. How many 5 draw poker hands are there? In 5 - card stud poker, the cards are dealt sequentially and the order of appearance is important. How many 5 - stud poker hands are there? b. How many hands of 5 - draw poker contain the ace of hearts? What is the probability that a 5 - card draw hand contains the ace of hearts?
  2. Suppose we roll two six-sided dice. Consider event A as getting an odd number on die 1, event B as getting an even sum for the two dice. Are event A and B independent?

a (^) An Introduction to Statistical Learning, James, G. et al (2013), Chapter 2

  1. An organization is planning a raffle to sell 40 tickets. Each customer can only buy one ticket. There are three prizes to be awarded. If each of the five organizers of the raffle buy one ticket, find out the following probabilities: a. The five organizers win all the prizes. b. The five organizers win exactly one of the prizes. c. The five organizers win none of the prizes.
  2. A spam filer is designed by screening commonly occurring phrases in spam. Suppose that 60% of email is spam. In 20% of the spam emails, the phrase “free gift card” is used. In non-spam emails, 99.5% of them do not mention “free gift card”. What is the probability that a newly arrived email which does mention “free gift card”, is not spam?