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Department of Mathematics
Math 151. Probability Spri=
ng
2012
Course Outline
Time and
Place: =
MWF 900 am - 950 am Millikan 134
Instruct=
or: =
Dr.
Adolfo J. Rumbos
Office:<=
/span> =
=
Andrew
259
Phone/e-=
mail: =
e=
xt. 18713 / arumbos@pomona.edu
Office
Hours: MWF 11:00 am – 11:50 am; T=
R 9:00
am – 10:00 am; or by appointment
Text: =
Probability
and Statistics,
by Morris H. DeGroot and Mark J.
Schervish, Adison Wesley
Prerequi=
sites: Multivari=
able
Calculus or Vector Calculus, and Linear Algebra.
Course
Description. This course is an
introduction to the theory and applications of Probability; special attenti=
on
will be given to applications relevant to statistical inference. A solid knowledge of multivariable
calculus and linear algebra will be presupposed. The course topics are listed in the
attached tentative schedule of lectures and examinations.
Assigned
Grading
Policy. Grades will be based on the
homework, three 50-minute examinations, plus a comprehensive final
examination. The overall scor=
e will
be computed as follows:
&=
nbsp; &nbs=
p; homework &=
nbsp; &nbs=
p; &=
nbsp;
&=
nbsp; 20%
&=
nbsp; &nbs=
p; three
50-minute exams &nbs=
p; &=
nbsp; &nbs=
p; 50%
&=
nbsp; &nbs=
p; final
examination &n=
bsp;  =
; &n=
bsp;  =
; 30%
Final
Examination.
Time: Thur=
sday,
May 10
9:00 am - 11:00 am.
Place: Millikan =
213
Math
151. Probability &=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; &=
nbsp; &nbs=
p; Spring
2012
Tentative Schedule of Lectures and
Examinations
Date &=
nbsp; &nbs=
p; Topic
W Jan 18 =
span>Introduction: A problem from statistical inferen=
ce
F &=
nbsp; Jan 20 =
span>Sample
Spaces
M &n=
bsp; Jan 23 =
span>σ-fields
W Jan 25 =
span>Probability
function
F &=
nbsp; Jan 27 Probability function
(continued)
M &n=
bsp; Jan 30 =
span>Independent
events
W Feb 1 Conditional
probability
F &=
nbsp; Feb 3&n=
bsp; Con=
tinuous
and discrete random variables
M &n=
bsp; Feb 6 Cumulative
distribution function (cdf)
W Feb 8 Probability
density function (pdf)
F &=
nbsp; Feb 10=
P=
robability
mass function (pmf)
M &n=
bsp; Feb 13=
E=
xpectation
of a random variable
W Feb 15=
R=
eview
F &=
nbsp; Feb 17=
<=
b>Exam
1
M &n=
bsp; Feb 20=
E=
xpectation
of a function of a random variable
W Feb 22=
V=
ariance
F &=
nbsp; Feb 24 Moments
M &n=
bsp; Feb 27=
M=
oment
generating function (mgf)
W Feb 29=
E=
xamples
of random variables
F &=
nbsp; Mar 2 &nbs=
p; Examples
of discrete distributions =
M &n=
bsp; Mar 5 &=
nbsp; Examples
of continuous distributions
W Mar 7 &nbs=
p; Joint
distribution functions
F &=
nbsp; Mar 9 &nbs=
p; Joint
distribution functions (continued)
M &n=
bsp; Mar
12  =
; Spring
Recess!
W Mar
14  =
; Spring
Recess!
F &=
nbsp; Mar
16  =
; Spring
Recess!
M &n=
bsp; Mar 19=
M=
arginal
distributions
W Mar 21=
M=
arginal
distributions (continued)
F &=
nbsp; Mar 23=
P=
roblems
Date &=
nbsp; &nbs=
p; Topic
M &n=
bsp; Mar.
26  =
; Review
W Mar 28=
<=
b>Exam
2
F &=
nbsp; Mar 30=
Cesar Chavez Day (no class)
M &n=
bsp; Apr 2 Independent
random variables
W Apr 4 mgf
convergence theorem
F &=
nbsp; Apr 6 The
Central Limit Theorem
M &n=
bsp; Apr 9 Simple
random samples
W Apr 11=
M=
ean
and variance of random samples
F &=
nbsp; Apr 13=
S=
ampling
distribution
M &n=
bsp; Apr 16=
C=
onditional
distribution
W Apr 18=
C=
onditional
expectation
F &=
nbsp; Apr 20=
C=
ovariance
and correlation &nbs=
p;
M &n=
bsp; Apr 23 C=
ovariance
and correlation (continued)
W Apr 25 R=
eview
F &=
nbsp; Apr 27 <=
b>Exam
3
M =
Apr 30 R=
eview
W May 2 Review
Th May 10=
Final
Examination