1. Express each of the following sums in summation notation

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=2and 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)(????12?2????3)+(????22?2????4)+(????32?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, wherexis the average number of hours worked per week by the student andyis the GPA the student achieved that term.

????=3.09?0.15???? ln(????)=1.56?0.46ln(????) ????=3.83?0.95ln (????) ln(????)=1.22?0.08????

a) Plot each of the functions forx= 2 tox= 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 atx= 7. State the interpretation of the slope.

c) Calculate the elasticity of each function atx= 7 and give the interpretation.

4. LetXbe a discrete random variable that is the value shown on a single roll of a fair die.

a) What is the expected value ofX? What is the expected value ofX2?

b) Find the variance ofX.

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

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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 ofX, the number of games per visit.

x	1	2	3	4	5	6	7
f(x)	.05	.05	.15	.25	.30	.15	.05