BUSS 230 Managerial Economics
Fall 2013 2014
Dr. George G. Namur
Midterm Review Problems
Problem 1
A firms total cost and total revenue functions are as follows:
a) Write an expression for the profit function (as a function of Q)
b) Determine the optimal
AMERICAN UNIVERSITY of BEIRUT
OLAYAN SCHOOL of BUSINESS
BUSS 230 Managerial Economics- Fall Semester 2006/07
FINAL EXAM January 18, 2007
NAME: _
ID: _
SECTION: _
INSTRUCTOR: _
ANSWER ALL QUESTIONS TIME ALLOWED: 2 hours
I.
Multiple choice - (24 points). On
CIVE210 Spring2014-2015
Quiz1
&A. El-Souri
Quiz.1
Spring 2014-2015
(March 11, 2015)
CIVE210 STATICS
CLOSED BOOK, 1 HR 30 Minutes
Name:
ID#:
NOTES
3PROBLEMS 12 PAGES.
ALL YOUR ANSWERS SHOULD BE PROVIDED ON THE QUESTION SHEETS.
TWO EXTRA SHEETS ARE PROVI
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American University of Beirut
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STAT 230
Introduction to Probability and
Summer 2006
,
and om' Variables
.
quiz # 2
Exercise 1 (6 points) Let X be a random a random variable with pdf
a. Find the cdf of X
b. Find P ( X
c. Find
< -1/2),
American University of Beirut
STAT 230
Introduction to Probability and Random Variables
Spring 25308
quiz # 2
Name: ID #:
circle your section please: 1 (TTH 8 am} 2 (TTH 2 pm)
1. In a lot of 10 light bulbs, there are 2 bad bulbs. An inspector examines 5 b
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American University of Beirut
STAT 230
Introduction to Probability and Random Variables
Summer 2006
quiz # 3
Exercise 1 There are 5 black chips and 3 white chips in a bowl. The black chips are numbered 1,1,1,2,2,
respectively, and the whi
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MIDTERH EXAM; STAT zoo Summer .E
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American University of Beirut
STAT 230
Introduction to Probability and Random Variables
Spring 2003
quiz 7% 1
Name: ID #:
circle your section please: 1 (TTH 8 am) 2 (TTH 2 pm)
Exercise 1 (20 points)
a. 3 history books, 4 math books, and 2 biology books ar
American University of Beirut
STAT 230
Introduction to Probability and Random Variables
Fall 2011
quiz # 1
1) A palindrome is a sequence of letters that reads
the same backwards as forwards (for example
aabaa and radar are palindrome; abb is not).
How man
American University of Beirut
8) In a squash tournament between three playSTAT 230
ers A, B and C, each player plays the othIntroduction to Probability and Random Variables
ers once (ie. A plays B, A plays C and B
Spring 2011
plays C). Assume the followin
American University of Beirut
5) Suppose that two fair dice have been tossed
STAT 230
and the total of their top faces is found to be
divisible by 5. Find the probability that both
Introduction to Probability and Random Variables
of them have landed 5
Spr
Uniform distribution
Let X be a random variable with pdf
f (x) =
1
, a < x < b (a < b)
ba
X is called uniform over the interval (a, b), denoted U(a, b)
Property
E (X ) =
a+b
2 ,
E (X 2 ) =
b 2 +ab+a2
,
3
and Var (X ) =
(ba)2
12
Exercise
Buses arrive at a
Sampling distributions
December 16, 2011
Sampling distributions
Sum of independent normal distributions
Proposition
Let X1 , X2 , . . . , Xn be n independent normal distributions with
respective means i and variance i2 , i = 1, 2, . . . , n
Then Y = a1 X1
Stat 230 - Midterm (Summer 10)
T. Tlas
=
Please answer all the questions on the same sheet of paper on which they are written. Any
part of your answer written on the wrong page will not be graded.
There are 6 problems in total. Some questions have sever
American University of Beirut
STAT 230
Introduction to Probability and Random Variables
Spring 2007
quiz # 2
Name:
.
ID #:
.
1. (10 points) A purchaser of electrical components buys them in lots of size 10. It is his
policy to inspect 3 components randoml
CIVEZIU Sgn'ng 2015-16 Quiz 2 M. Mabsam
QUIZ 2
Spring 2015-16
(Tuesday April 19, 2016)
CIVE210 - STATICS
CLOSED BOOK, 1 HR 30 MN
Name: [@cfw_ . '/ E ID#: ; is; J 1 Section: g
NOTES
0 2 PROBLEMS 12 PAGES.
0 ALL YOUR ANSWERS SHOULD BE PROVIDED ON THE QU
American University of Beirut
STAT 230
Introduction to Probability and Random Variables
Summer 2010
7. Let (X, Y ) be a couple of random variables
with joint pdf
f (x, y) = e(x+y) , x > 0 , y > 0
Let U = X + Y and V = X/Y .
Final Exam
a. Find the joint pd
Stat 230 - Final (Summer 10)
T. Tlas
=
Please answer questions 1,2,3,5 and 6 on the same sheet of paper on which they are written.
Question 4 has an additional sheet for you to write you answer on. Any part of your answer
written on the wrong page will n
American University of Beirut
STAT 230
Introduction to Probability and Random Variables
Fall 2007
Final Exam
Name:
.
ID #:
.
Exercise 1 Let X1 , X2 , X3 be three independent random variables with binomial distributions
b(4, 1/2), b(6, 1/3), and b(12, 1/6)
American University of Beirut
STAT 230
Introduction to Probability and Random Variables
Summer 2007
quiz # 1
Exercise 1 a. (7 points) A cafe lets you order a deli sandwich your way. There are 6 choices
for bread, 4 choices for meat, 4 choices for cheese,
American University of Beirut
STAT 230
Introduction to Probability and Random Variables
Fall 2007-2008
quiz # 1
Name:
.
ID #:
.
Exercise 1 a. (4 points) A total of 7 dierent gifts are to be distributed among 10 children.
How many distinct results are poss
American University of Beirut
STAT 230
Introduction to Probability and Random Variables
Fall 2007-2008
quiz # 2
Name:
.
ID #:
.
Exercise 1 (25 points) Let X be a random a random variable with pdf
1/2 0 < x < 1
f (x) =
1/2 2 < x < 3
0
elsewhere
a. nd the
Special discrete random variables
Bernoulli distribution
A Bernouilli random variable is a variable that assumes exactly two
values, 1 for success and 0 for failure.
Special discrete random variables
Bernoulli distribution
A Bernouilli random variable is
Transformation of random variables
December 6, 2011
Transformation of random variables
Example
Let X be a discrete random variable with pdf
x
-1
0
1
f(x)
1/4
1/2
1/4
a) Find the pdf of Y = 2X 1
b) Find the pdf of Y = X 2
Transformation of random variables
November 19th 2009
STAT 230
TEST 1
A. Alhakim
PART I.
Multiple Choice Questions. Answer the following questions by circling the best possible answer.
Exactly one answer must be circled.
1. Which of the following statements is correct?
(a)
(b)
(c)
(d)
If A
.62. /2/0;3 I Prof. Vacuum!
AMERICAN UNIVERSITY of BEIRUT
OLAYAN SCHOOL of BUSINESS
BUSS 230 MANAGERIAL ECONOMICS
FINAL EXAM June 11, 2005
NAME: II):
SECTION: INSTRUCTOR:
ANSWER ALL QUESTIONS TIME ALLOWED: 2 hours
I. Multiple choices - 124 points;. On thi
BUSS 230 - Final Exam : January 22, 2008
I. Multiple Choice
1
2
3
4
D
A
C
B
5
6
7
8
A
B
B
A
9
10
11
12
C
C
D
D
II. True or False
1.
TRUE
Before inflection point, TVC will be increasing at a decreasing rate and hence MC will be
falling. Beyond inflection p
CIVE210 Spring 2015-16
Quiz 2
M. Mabsout
QUIZ 2
Spring 2015-16
(Tuesday April 19, 2016)
CIVE210 STATICS
CLOSED BOOK, 1 HR 30 MN
Name:
ID#:
Section:
NOTES
2 PROBLEMS 12 PAGES.
ALL YOUR ANSWERS SHOULD BE PROVIDED ON THE QUESTION SHEETS.
THREE EXTRA SHEET
CIVE210 Fall 2014-2015
Quiz1
F. El-Meski &A. El-Souri
Quiz.1
Fall 2014-2015
(October 22, 2014)
CIVE210 STATICS
CLOSED BOOK, 1 HR 15 Minutes
Name:
ID#:
NOTES
3PROBLEMS 10 PAGES.
ALL YOUR ANSWERS SHOULD BE PROVIDED ON THE QUESTION SHEETS.
TWO EXTRA SHEET
STAT 230. Test 2 -Spring 2015
Name:
Lecturer:
Decide whether the following statements are true (T) or false (F).
Each correct answer will be awarded 2 points. No penalty for wrong
answers.
T
F
Corr(X, 4 3 X) = 1 for any random variable with positive varia
Combinatorics
Notation
n!
Cnk
Pnk
n (n 1) (n 2) 3 2 1
Pk
n
n!
= n
=
=
k!(n k)!
k!
k
n!
= (n)k =
= k!Cnk
(n k)!
=
Drawing a sample of size k from an urn containing n balls
ai , label of the ball selected at i-th step: ai = 1, . . . , n
n+k1
k
with replac