Download Week 1. Axiomatic definition of probability. Probability space

MATH 392 Probability Theory and Statistics
(4-0) 4 Credits
Spring Semester 2009-2010
Instructor: Prof. Dr. Sofiya Ostrovska
Office: 412 FEF
Phone: 8211
E-mail: [email protected]
Office Hours: To be announced
Course Outline: Probability space. Independence and conditional probability. Random
variables and probability distributions. Numerical characteristics of random variables.
Classical probability distributions. Sampling. Point estimation. Interval estimation.
Hypotheses testing.
Text Book: M.H. DeGroot, M.J. Shervish. Probability and Statistics. Addison
Wesley, 2002
References: W.Feller. An Introduction to probability theory and its applications, v.I,II.
J.Wiley and Sons, New-York
J.E. Freund, R.E. Walpole. Mathematical Statistics. Prentice Hall, 1987
Course Topics:
Week 1. Axiomatic definition of probability. Probability space. Classical probability.
Uniform space.
Week 2. Independence of two and several events. Pairwise independence. Law of total
probability. Bayes’ theorem.
Week 3. Independent experiments. Bernoulli trials.
Week 4. Random variables. Distribution of a random variable and a distribution
function. Discrete, absolutely continuous, and singular distributions.
Week 5. Numerical characteristics of random variables. Mathematical expectation and
variance, their properties. Chebyshev inequality.
Week 6. Classical random variables. Their properties and applications.
Week 7. Random vectors. Distribution of a random vector and distribution of its
projections. Independent random variables.
Weeks 8. Organization and description of data. Frequency distributions, their graphic
presentations. Parameters and statistics.
Week 9: Special probability distributions. Moment-generating functions.
Week 10: The Central Limit Theorem, its applications.
Week 11: Point estimation. Unbiased, consistent, sufficient estimators.
Week 12: Interval estimation. Confidence intervals.
Week 13: Statistical hypotheses. Simple and composite hypotheses. Null and
alternative hypotheses.
Week 14: Testing statistical hypotheses. Type I and II errors. Level of significance.
Week 15: Tests concerning means, proportions, and variances. Survey of the Course.
Attendence: You must attend classes and tests. Attendence to can not be less than 80 %.
Lectures: You are expected to keep silence unless you have a question. You are
encouraged to ask questions as soon as something is unclear to you. Even if you have
the textbook, you must take lecture notes.
Exams: Two mid-term exams and a final exam will be given. Also quizes and
homeworks will be assigned during the semester. No make-up exams will be given
unless proper documentation for the absence is received. (Excuse must be approved by
the university)
Academic Dishonesty: No cheating during the exams and in the HW assignments is
allowed. Cheating includes but not limited to both providing and copying information
during the exams and in homework assignments. It is considered as a discipline
violation. Hence in case of cheating, both parts will certainly get a score of zero from the
corresponding exam and homework, and disciplinary action will be applied.
Homework Assignments:
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Homework assignments have an important role in understanding and practicing
the subject we discuss in the classroom. That’s why try to do your homework
assignments and exercises first of all for your own favour.
The homework assignments must be submitted by everyone till the end of the
due date and hour. Late submissions will not be accepted.
Assignments must be done individually.
As mentioned above, both taking and giving copies in HW assignments will be
treated the same. If a copy action is recognized, the actual grade of the
homework assignment will get a score of zero.
Grading Policy: Final score is counted according to the following scheme:
Quizes+HW
MT Exams
Final Exam
20 %
40 % (20%+20%)
40 %
You will have a two-day period after the scores are announced for objection.
Midterm Exams : Midterm I March 24, 2010
Midterm II May
5, 2010
13:30 - 15:20
13:30 - 15:20