Name
Printed: November 19, 2013
MATH 4008 Quiz-9 Answer Key
Be sure to show your work. No credit for inspired answers!
1. A company manufactures a brand of light bulb with a lifetime in months that is normally distributed with mean 3 and
variance 1. A con
SYLLABUS FOR INTRODUCTION TO PROBABILITY
(MATH4008)
This is a detailed syllabus for Introduction to Probability (MATH4008) at University of Cincinnati, Fall semester, 2014. Below listed are the required reading
materials (subtitles) from each chapter of t
Math 4008, Fall 2014
Homework 7
Homework due Nov 3 Mon. Problems with are recommended but not
required.
Reading: Textbook1 Chapter 6.1, 6.2.
Hand-in Problems.
Textbook Chapter 6.1, Exercises 2, 4, 14, 22; Chapter 6.2, Exercises
2, 8, 12, 14.
Not hand-i
Math 4008, Fall 2014
Sample Quiz 2
Name
1. On Halloween, Mr. and Mrs. Smith gave out 100 (indistinguishable)
candies to 10 kids from the neighbor area. It might happen that a kid
came too late so that the candies had been all gone already.
(a) How many di
Math 4008, Fall 2014
Quiz 2
Name
The total time for this quiz is 55 minutes. Show steps clearly.
1. We are interested in how to schedule all the regular season games of
an NBA team, say San Antonio Spurs, the defending champion. The
Spurs have 82 regular
Math 4008, Fall 2014
Sample Problems for Final Exam
Final exam: Dec. 8, Mon, 1:30-3:30pm. There will be 8 problems in total.
Below are a few sample problems.
1. State the following definitions and results.
Distribution function of a discrete random variab
Math 4008, Fall 2014
Midterm Exam
Name
There are 6 problems, total 30 points. Present your solutions clearly.
You may provide
formulae using factorials (n!) and binomial co
n
efficients ( j ) as solutions. No need to simplify nor to calculate
the expressi
Math 4008, Fall 2014
Homework 6 Solution
4.2.2
R 10
0.1e0.1t dt
e0.1 e1
=
= 1 e0.9 .
(a) R1
0.1
0.1t dt
e
0.1e
1
R 10
0.1e0.1t dt
e0.5 e1
(b) R5
=
= 1 e0.5 .
0.5
0.1t dt
e
0.1e
5
For the first two parts, one can also get the answer by memoryless
property
Math 4008, Fall 2014
Quiz 2 Solutions
Name
The total time for this quiz is 55 minutes. Show steps clearly.
1. We are interested in how to schedule all the regular season games of
an NBA team, say San Antonio Spurs, the defending champion. The
Spurs have 8
Math 4008, Fall 2014
Sample Quiz 2
Name
1. On Halloween, Mr. and Mrs. Smith gave out 100 (indistinguishable)
candies to 10 kids from the neighbor area. It might happen that a kid
came too late so that the candies had been all gone already.
(a) How many di
Math 4008, Fall 2014
Sample Problems for Final Exam
Final exam: Dec. 8, Mon, 1:30-3:30pm. There will be 8 problems in total.
Below are a few sample problems.
1. State the following definitions and results.
Distribution function of a discrete random variab
Math 4008, Fall 2014
Homework 6 Solution
6.3.2
(a) Observe that the p.d.f. is symmetric with respect to zero (fX (x) =
fX (x), thus the random variable has zero mean. For the variance,
1
Z
2
Var(X) = E(X ) =
3
x2 (1 x2 )dx
4
1
Z 1
Z 1
3 2
3 4
1
3
1
=
x d
Math 4008, Fall 2014
Homework 4
Homework due Sep 29 Mon in class. Problems with are recommended
but not required.
Reading: Textbook1 Chapter 3.2.
Hand-in Problems: You may give your final results in terms of factorials and combinatorial numbers.
1. Text
Math 4008, Fall 2014
Homework 6
Homework due Oct 15 Wed. This time no need to hand in homework
in class; instead I will post solutions on Oct 15 Wed. Problems with are
recommended but not required.
Reading: Textbook1 Chapter 4.2.
Hand-in Problems (no ha
Name
Printed: November 23, 2013
MATH 4008 Quiz-10 Answer Key
Be sure to show your work. No credit for inspired answers!
1. A company manufactures a brand of light bulb with a lifetime in months that is normally distributed with mean 3 and
variance 1.
A co
Saab Online Testing
http:/www.saab.org/actuarialmuorg.cgi
You did 5 problems right out of 30 problems selected randomly. Your score is 17 percent
Do not resubmit the last test.
Push here to repeat the test with the same problems
Push here to repeat the mi
Name
Printed: November 9, 2013
MATH 4008 Quiz-8 Answer Key
Be sure to show your work. No credit for inspired answers!
1. A company oers a basic life insurance policy to its employees, as well as a supplemental life insurance policy. To
purchase the supple
Printed: November 9, 2013
Name
MATH 4008 Quiz-7 Answer Key
Be sure to show your work. No credit for inspired answers!
1. Let X be a normal random variable with mean 1 and variance 4. Compute Pr(X 2 2X 8)
Answer Solving the inequality, we need Pr(X 1)2 9 =
Name
Printed: September 6, 2013
MATH 4008 Quiz-2 Answer: Key
Be sure to show your work. No credit for inspired answers!
1. Among a large group of patients recovering from shouder injuries, it is found that 22% visit both a physical therapist
and a chiropr
Printed: September 14, 2013
Name
MATH 4008 Quiz-3 Answer: Key
Be sure to show your work. No credit for inspired answers!
1. A blood test indicates the presence of a particular disease 95% of the time when the disease is actually present. The
same test ind
Name
Printed: October 7, 2013
MATH 4008 Quiz-5 Answer Key
Be sure to show your work. No credit for inspired answers!
1. A fair die is tossed until the rst 5 appears. Let X denote the random variable equal to the number of tosses required.
Compute E
1
5X
.
Printed: August 30, 2013
Name
MATH 4008 Quiz-1 Answer: Key
Be sure to show your work. No credit for inspired answers!
1. A marketing survey indicates that 60% of the population owns an automobile, 30% owns a house, and 10% owns both
an automobile and a ho
Math 4008, Fall 2014
Homework 2
Homework due Sep 15 Mon in class. Problems with are recommended
but not required.
Reading: Textbook1 Chapter 2.2.
Hand-in Problems: several problems below require calculating integral
and double integrals. Show full steps
Math 4008, Fall 2014
Homework 3
Homework due Sep 22 Mon in class. Problems with are recommended
but not required.
Reading: Textbook1 Chapter 3.1.
Hand-in Problems: You may give your final results in terms of factorials.
1. Textbook Chapter 3.1, Exercise
Math 4008, Fall 2014
Homework 1
Homework due Sep 5 Fri in class. Problems with are recommended but
not required.
Reading: Textbook1 Chapter 1.2.
Hand-in Problems:
1. Textbook Chapter 1, Exercises 6, 8, 10, 14, 16, 18 (a), 20.
R
2. Compute 0 x2 ex dx. Sh
Math 4008, Fall 2014
Homework 5
Homework due Oct 6 Mon in class. Problems with are recommended
but not required.
Quiz 1: Problems in Quiz 1 that you did not find the correct answers.
Hand in your new solutions with your Quiz 1 answer sheet together.
Rea
Math 4008, Fall 2014 Midterm Exam
Name
There are 6 problems, total 30 points. Present your solutions clearly.
You may provide formulae using factorials (n!) and binomial co
efcients (731) as solutions. No need to simplify nor to calculate
the expression