M 362K Probability I
Unique# 56265 Fall
2012
Instructor:
Prof. Irene M. Gamba
Office: RLM 10.166, Phone: 471-7150
E-Mail: gamba@math.utexas.edu
Office hours: Tuesday 2:15 to 3:15 pm
Textbook:
Probability
by
Jim Pitman
Meeting Hours:
T-Th 12:30-1:45pm RLM 5.120
Optional Discussion Hour with Chenglong Zhang:
Wednesdays 5:00 to 7:00 pm RLM 10.176
Prerequisites and degree relevance:
M408D with a grade of at least C. A student may not receive credit for M316 after completing
M362K with a grade of C or better.
Course description:
This is an introductory course in the mathematical theory of probability, and is fundamental to
further work in probability and statistics. Axioms for probability are used to derive
probability densities and distribution functions. Basic combinatorics (counting) is introduced
to handle some problems. Properties associated with a random variable are developed for the
usual elementary distributions. Fundamental limit laws like the law of large numbers (LLN) and
central limit theorem (CLT) are discussed. To develop a thorough understanding of course
material, both problem solving and theorem proving are required.
Material to cover: Chapters
1 to 6
Course Outline:
Introduction:
Equally likely outcomes, events and probability. Distributions, conditional
probabilities and independence, Bayes' rules
Repeated trials and sampling:
Binomial distributions, normal and Poisson approximations, random sampling
Conditional
Probability, Bayes' Theorem, and Independent Events.
Random Variables: expectations,
variance, standard deviation and normal approximation, discrete and Poisson distributions
Continuous distributions:
Probability densities exponential and Gamma distributions, hazard rates, change of variables
cumulatives.
Continuous joint distributions:
densities and independent normal variables.
Dependence: Conditional
distributions and expectations, discrete and continuous cases. Covariance, correlations
and bivariate normal.
TESTS: There will be 2 in-class midterms (100pts. each) that are scheduled
for the dates:
First midterm Thursday October 11, 2012
Second Midterm Tuesday December 4, 2012 ,
Save these two dates. No Make-up midterms
will be given.
A comprehensive final examination (200 pts.) will be administered on the
date and at the time that is officially assigned to this class in the course
schedule.
FINAL EXAM: Monday, December 17, 2012,
2:00–5:00 pm.
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Location: TBA
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Students: Log on with your UT EID to
view your personal
final exam schedule for all your current classes.
Implicit
in your registration for this class is the affirmation
that, barring some unforeseen calamity, you will be present to take the final
examination at this time.
GRADING POLICY
100 points Homework
200 points Midterms (2)
200 points Final (Comprehensive)
If your cumulative grade from the midterms and homework is below 170 pts,
you must take the final exam. Above 170 points you may wish to take the final,
depending on your grade.
Above 170 points,
above 245 A grade
from 235-244 A- grade
from 225-235 B+ grade
from 200-225 B grade
from 190-199 B- grade
from 180-190 C+ grade
from 170-180 C grade
The final exam score will be added up to your accumulated grade from the
midterms and homework. In this case the grade distribution is
above
375
A grade
from 365-374 A- grade
from 355-364 B+ grade
from 315-364 B grade
from 305-314 B- grade
from 295-304 C+ grade
from 265-294 C grade
from 255-264 C- grade
from 245-254 D+ grade
from 225-244 D grade
below 225
F grade
Exam policy:
Calculators and books are not permitted during quizzes, midterms, and the final exam. A valid
photo ID must be available to be checked at all exams. Make-up exams will not be given so
please remember the appropriate exam dates. In extraordinary circumstances ONLY, the final exam
score will compensate for a missing midterm exam. This includes illness, observance of a
religious holiday, or a university-related absence (e.g., away game) with 2 weeks advance
notice. Proper documentation (such as a doctor's note) is required in all cases.
Honor code:
The core values of the University of Texas at Austin are learning, discovery, freedom,
leadership, individual opportunity and responsibility. Each member of the university is
expected to uphold these values through integrity, honesty, trust, fairness and respect toward
Please, make sure that cell phones and
laptops are turned off.
The University of Texas at Austin
provides upon request appropriate academic accommodations for qualified
students with disabilities. For more information, contact the Office of the
Dean of Students at 471-6259, 471-4641 TTY.
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