Theory (60 points)
1. (1) Explain what is wrong with the following statements, and (2) co
ect it.
a. There is a chance 60% of purchasing item A and 75% of purchasing item B, and purchasing item A and B is independent. Then there is a 135% chance of purchasing both items. (10 points)
. 80% of our graduate students are working on companies. Of the students working on companies, only 10% are working on FANNG. Hence, 70% of our graduate students are working on companies except for FANNG. (10 points)
2. Three professors at George Washington University experimented to determine if economists are more selfish than other people. They dropped 64 stamped, addressed envelopes with $10 cash in different classrooms on the George Washington campus. 44% were returned overall. From the economics classes, 56% of the envelopes were returned. From the business, psychology, and history classes 31% were returned. Let: R = money returned; E = economics classes; O = other classes
a. Write a probability statement for the overall percent of money returned. (2 points)
. Write a probability statement for the percent of money returned out of the economics classes. (2 points)
c. Write a probability statement for the percent of money returned out of the other classes. (2 points)
d. Is money being returned independent of the class? Justify your answer numerically and explain it. (2 points)
e. Based upon this study, do you think that economists are more selfish than other people? Explain why or why not. (2 points)
3. At a college, 72% of courses have final exams and 46% of courses require research papers. Suppose that 32% of courses have a research paper and a final exam. Let F be the event that a course has a final exam. Let R be the event that a course requires a research paper.
a. P(F ∩ R) and P(F U R). (2 points)
. Find the probability that a course has a final exam or a research project (just a number). (4 points)
c. Find the probability that a course has NEITHER of these two requirements (just a number). (4 points)
4. You have 10 blue tiles, 5 red tiles, and 5 green tiles (without replacement).
a. How many patterns can you make with these tiles? (10 points)
. How many patterns can you make starting with blue? (10 points)
Practice (40 points)
1. Find “UniversalBank.csv” and load it using pandas.
2. Show how many data you have through dataframe. (5 points)
3. Show its descriptive statistics. (5 points)
4. Pick only Age, Experience, Income, Family, Education, and PersonalLoan. (10 points)
5. Show the descriptive statistics and draw histograms for PersonalLoan = 0. (5 points)
6. Show the descriptive statistics and draw histograms for PersonalLoan = 1. (5 points)
7. Which factor(s) (Age, Experience, Income, Family, and Education) is meaningful to distinguish status of PersonalLoan based on histograms? (10 points)