NORTHWESTERN UNIVERSITY DEPARTMENT OF ECONOMICS WINTER 2012 ECONOMICS 202: INTRODUCTION TO MICROECONOMICS Instructor: Office: Office hours: Office phone: e-mail: Professor Martin Zelder Andersen 348 M 2-3 pm; T 1:30-3 pm; W 5-6 pm; and by appointment 847-

IEMS 202
Midterm # 1
Formula Sheet
(E c )c = E
EE =E
EE =E
EE
Sc =
c = S
E Ec =
E Ec = S
ES =E
E=E
ES =S
E=
E
ES
E (F G) = (E F ) (E G)
E (F G) = (E F ) (E G)
(E F )c = E c F c
(E F )c = E c F c
F (ni=1 Ei ) = ni=1 (F Ei )
E = (E F )

1
DO NOT DISTRIBUTE
IEMS 202
Probability
Fall 2015
November, 2015
Midterm Exam 2 - Exercise
Note: For best practice experience:
1. First learn the material from the lecture and the attempt these problems.
2. Try to solve these problems under time pressure

Industrial Engineering & Management Sciences 202
Probability
Fall 2015
October 21, 2015
Homework Assignment 3
Due: October 28, 2015, 8pm on Canvas
1. Let X represent the difference between the number of heads and the number of tails obtained when a
coin i

1
IEMS 202
Probability
Midterm Exam 1 - Exercise - Solutions
1. Two fair dice are tossed sequentially. F the event that the first die is a 4.
a) E1 the event that the sum is 6. Compute to determine of E1 and F are independent.
b) E2 the event that the sum

Industrial Engineering & Management Sciences 202
Probability
Fall 2015
November 9, 2015
Homework Assignment 5
Due: 17 November 2015, 8pm on Canvas
1. If X is uniform over (0, 1), calculate E[X n ] and V ar(X n ).
2. Let X and Y each take on either the val

Industrial Engineering & Management Sciences 202
Probability
Fall 2015
October 28, 2015
Homework Assignment 4
Due: 4 November 2015, 8pm on Canvas
1. You have $100, and a certain commodity presently sells for $2 per ounce (market price). Suppose that
after

Industrial Engineering & Management Sciences 202
Probability
Fall 2015
November 18, 2015
Homework Assignment 7
Due: 24 November 2015, 8pm on Canvas
1. Let X1 , X2 , ., X10 be independent Poisson random variables with mean 1.
(a) Use the Markov inequality

1
Name:
IEMS 202
Probability
Midterm Exam 1 - Exercise
Note: For best practice experience:
1. first learn the material from the lecture and the attempt these problems.
2. try to solve these problems under time pressure
3. tackle these problems without ref

IEMS 202
Midterm # 1
Formula Sheet
(E c )c = E
EE =E
EE =E
EE
Sc =
c = S
E Ec =
E Ec = S
ES =E
E=E
ES =S
E=
E
ES
E (F G) = (E F ) (E G)
E (F G) = (E F ) (E G)
(E F )c = E c F c
(E F )c = E c F c
F (ni=1 Ei ) = ni=1 (F Ei )
E = (E F )

IEMS 202
Homework # 1
Winter 2017
Due: Wednesday, January 11 at NOON.
1. Three people play one round of the rock-scissors-paper (R-S-P) game. For convenience, we will
say outcome RPS (for example) represents player 1 choosing rock, player choosing paper,

IEMS 202
Homework # 3
Winter 2017
Due: Wednesday, January 25 at NOON.
For each of the following problems, show your work and explain your reasoning.
1. An article in The Atlantic includes the following paragraph (you can find the full article at http:
/ww

IEMS 202: Probability
Winter 2016
Practice Midterm Exam 1
Page 1 of 4
Solutions to the Practice Midterm Exam 1
Problem 1.
1. Let A be the set
A = cfw_a, b, c, d.
Give the cardinality of A, and the power set of A.
2. Let B be a set of cardinality n.
(a) Gi

IEMS 202 - Probability
Winter 2016
Homework 1
Page 1 of 2
Homework 1 (due Friday 1/15)
Exercise 1
Consider the sets
n
o
A = 1, 5, 3, red ;
n
B = 9.1, blue, 1, 5.
1. Give the power-set of A;
2. Give A B;
3. What is the relationship between the objects 1 an

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Industrial Engineering & Management Sciences 202
Probability
Spring 2017
March 31, 2017
Homework Assignment 1 Solution
Not for distribution
1. (see problem set)
Solution
(a) By the generalized basic principle of counting there are
26 26 26 10 10 10 10 10

Industrial Engineering & Management Sciences 202
Probability
Spring 2017
March 31, 2017
Homework Assignment 1
Due: April, 7 2017, 8pm and on Canvas as PDF.
1.
(a) How many different 8-digit password are possible if the first 3 digits are for letters and t

These are some optional problems in addition to the homework problems. However, they do
not cover all possible questions that could be on the exam. Solutions will not be provided.
Chapter 5
5.8 Consider the pu

IEMS 202
Homework # 2
Winter 2017
Due: Wednesday, January 18 at NOON.
For each of the following problems, show your work and explain your reasoning.
1. A license plate consists of two letters followed by three numerical digits (e.g. MX556).
(a) How many d

IEMS 202
Homework # 5
Winter 2017
Due: Wednesday, February 15 at NOON.
For each of the following problems, show your work and explain your reasoning.
1. You have decided to call Senator Paul Ryans office to express your opinion about the current
supreme c

IEMS 202
Homework # 4
Winter 2017
Due: Wednesday, February 8 at NOON.
For each of the following problems, show your work and explain your reasoning.
1. Five men and five women are ranked according to their scores on an examination. Assume that
no two scor

Industrial Engineering & Management Sciences 202
Probability
Fall 2015
November 27, 2015
Homework Assignment 7
(Bonus: this assignment is voluntarily and can replace a previous HW)
Due: 2 December 2015, 8pm on Canvas
1. (25 points ) X is a Poisson distrib

Industrial Engineering & Management Sciences 202
Probability
Fall 2015
Homework Assignment 1
Due: October, 7 2015, 8pm on Canvas as PDF.
1.
(a) How many different 8-digit password are possible if the first 3 digits are for letters and the other
5 for numb