MATH 501 Fall 2011
HW 3
Due Class #4 at the class break
DIRECTIONS: The directions are the same as the HW 1 directions. The collaboration policy from the syllabus
applies to this assignment and to all assignments.
On the rst page of this assignment, near
Some HW questions and answers

NOTE: I've decided to paraphrase the questions
this time; in some cases the wording
of the questions gave away something about
the answer, so this seems to be a better
approach.
Ex 1) What program do I use to run that
s
Math 501: Notes Set 7
1
Introduction to expected value for discrete random variables
Denition 1 If X is a discrete random variable with underlying
set fx1 ; x2 ; x3 ; : : :g ; we dene
X
E (X) =
xi pX (xi )
(1)
i
=
X
i
xi P (fX = xi g) :
(2)
If (and only i
Math 501: Notes Set 5
The pmf for B (n; p) is legitimate
1
For convenience, we quickly recall our denition from Notes Set 4:
Denition 1 (Binomial RVs) Suppose ( ; F; P ) is a probability space, and that X is a discrete random
variable on : Let pX denote t
Math 501: Notes Set 1
. since in action it frequently happens that no delay is permissible, it is very certain that,
when it is not in our power to determine what is true, we ought to act according to what is most
probable
 Ren Descartes, Discourse on Me
Math 501: Notes Set 6
Throughout these notes, suppose ( ; F; P ) is a probability space,
where is the sample space for a random experiment, F is the eld of events, and P is a probability measure on F:
1
Image, inverse image, and invertibility
Quite genera
Math 501: Notes Set 5
The pmf for B (n; p) is legitimate
1
For convenience, we quickly recall our denition from Notes Set 4:
Denition 1 (Binomial RVs) Suppose ( ; F; P ) is a probability
space, and that X is a discrete random variable on : Let pX denote
t
Math 501: Notes Set 1
. since in action it frequently happens that no delay is permissible, it is very certain that, when it is not in our power to
determine what is true, we ought to act according to what is most
probable
 Ren Descartes, Discourse on Me
Math 501: Notes Set 4
1
Random variables: an introductory example
We will begin with a simple example and introduce technical details gradually.
Example 1 A random experiment consists of ipping a fair coin four times. Let X represent the
number of heads.
Math 501: Notes Set 2
1
A little history
Probability theory has been widely used in many elds, such as economics, biology, epidemiology,
medicine, physics, genetics, chemistry, psychology, sociology, actuarial science, quality control, and
gaming theory,
Math 501: Notes Set 2
1
A little history
Probability theory has been widely used in many elds, such as economics, biology, epidemiology, medicine, physics, genetics, chemistry, psychology, sociology, actuarial science, quality control, and
gaming theory,
MATH 501 Fall 2011
HW 2
Due Class 3 at the beginning of class
DIRECTIONS: The directions are the same as the HW 1 directions. The collaboration policy from the syllabus
applies to this assignment and to all assignments.
On the rst page of this assignment,
MATH 501 Fall 2011
HW 7
Due next class (10/31 for Section 1, 11/2 for Section 2).
DIRECTIONS: The directions are the same as the HW 1 directions. The collaboration policy from the syllabus
applies to this assignment and to all assignments.
On the rst page
MATH 501 Fall 2011
HW 5
Due at the beginning of (or before) the Exam 1 review next Wednesday. If you cannot attend the
review, then leave your assignment under my o ce door prior to 5 p.m. on the night of the review,
or else email your assignment to me in
MATH 501 Fall 2011
HW 8
Due next class (11/7 for Section 1, 11/9 for Section 2).
DIRECTIONS: The directions are the same as the HW 1 directions. The collaboration policy from the syllabus
applies to this assignment and to all assignments.
On the rst page
MATH 501 Fall 2011
HW 6
Due at the class break next class (a week after the exam).
DIRECTIONS: The directions are the same as the HW 1 directions. The collaboration policy from the syllabus
applies to this assignment and to all assignments.
On the rst pag
MATH 501 Fall 2011
HW 1
Due at the beginning of Class #2 (in your section)
DIRECTIONS:
This HW will be collected and graded. Be sure to read the syllabus carefully. The section on collaboration applies
to this assignment and to all subsequent assignments.
MATH 501 Fall 2011
HW 4
Due Class #5 at the class break
DIRECTIONS: The directions are the same as the HW 1 directions. The collaboration policy from the syllabus
applies to this assignment and to all assignments.
On the rst page of this assignment, near
Some solutions to problems from our book:
7.35 For concreteness, lets imagine that the seats are numbered from 1 through
N on each side of the table. For each i = 1; 2; : : : ; N; dene the random variable
Xi as follows: Xi = 1 if the ith man is seated opp