02 Jun Question Economics 395 Spring 2014 Due May 29th, 2014, before 3 pm Assignment #1 1
Question
Economics 395 Spring 2014
Due May 29th, 2014, before 3 pm Assignment #1
1
Due Thursday, May 29th, by 3 pm in the Economics Office, SS 454. The office is
closed during lunch hour, noon – 1 pm.
Please remember to do a cover sheet with your name(s), the course number, number all the
pages, clearly label which question and part you are answering, and staple your
assignment.
1. Express each of the following sums in summation notation and then compute where
possible. Let X take the values ????1 = ?2, ????2 = ?1, ????3 = 0, ????4 = 1, ????5 = 2 and Y take the
values ????1 = ?1, ????2 = ?0.5, ????3 = 0, ????4 = 1, ????5 = 1.5.
a) ????1 + ????2 + ????3 + ????4 + ????5
b) ????3 + ????4 + ????5
c) (????1 ? ????1) + (????2 ? ????2) + (????3 ? ????3) + (????4 ? ????4) + (????5 ? ????5)
d) 2(????1 ? ????2) + 2(????2 ? ????3) + 2(????3 ? ????4)
e) (????2/????1) + (????3/????2) + (????4/????3)
f) (????1
2
? 2????3) + (????2
2
? 2????4) + (????3
2
? 2????5)
2. Show that ? (???????? ? ?????
????
????=1
) (???????? ? ?????) = ? ????????
????
????=1 ???????? ? ???????????????
3. An economist was trying to address the growing concern for educators about the number
of students who have part-time jobs while they attend high school. To help acquire
information, she recorded the average number of hours worked per week and the GPA
achieved for 200 students with part time jobs. Below are four equations that were
estimated by the economist with the data, where x is the average number of hours worked
per week by the student and y is the GPA the student achieved that term.
???? = 3.09 ? 0.15????
ln(????) = 1.56 ? 0.46 ln(????)
???? = 3.83 ? 0.95ln(????)
ln(????) = 1.22 ? 0.08????
a) Plot each of the functions for x = 2 to x = 12 on the same graph. Comment on
what you observe when you look at the functions on the graph.
b) Calculate the slope of each function at x = 7. State the interpretation of the slope.
c) Calculate the elasticity of each function at x = 7 and give the interpretation.
4. Let X be a discrete random variable that is the value shown on a single roll of a fair die.
a) What is the expected value of X? What is the expected value of X
2
?
b) Find the variance of X.
c) What is the probability of X=2 or X=3?
d) Find the expected value and variance of W if W = g(X) = 4X + 2.Economics 395 Spring 2014
Due May 29th, 2014, before 3 pm Assignment #1
2
e) Now, assume the die has been weighted so that P(X=1) = 1/3, P(X=2) = P(X=3) =
P(X=4) = 1/12, P(X=5) = 1/6, P(X=6) = 1/4. Find the answers to part a) and b)
under the new assumption.
5. After watching a number of children playing games in a video arcade, a statistics
practitioner estimated the following probability distribution of X, the number of games per
visit.
x 1 2 3 4 5 6 7
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