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SYLLABUS
THE THEORY of PROBABILITIES and MATHEMATICAL STATISTICS
MAT 307 ID 3215 (MAT 306 ID2619)
Spring- 2014
Lectures:
Elmira Tursunbekovna Musuralieva, Kandidat nauk on Physics and Mathematics,
Professor, elmiratm@mail.auca.kg;
Polina Sergeyevna Dolmatova, Kandidat of Technical Sciences, Assistant Professor,
dolmatova_p@mail.auca.kg.
Class meetings: 2 classes per week, total 3 credits, 15 working weeks.
Office hours: according to the individual schedules of the instructors. Office: 332/1,
phone: 66-15-47.
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Short course description:
This course will introduce you to the basic tools of theory of probability and statistics
with applications to social sciences and business. The course consists of the following
themes: counting techniques; basic probability concepts and theorems; discrete and
continuous probability distributions; statistical inference and sampling, the central limit
theorem, confidence intervals for the mean of a normal population, hypothesis testing
for the mean of a normal population.
Prerequisites: MAT 131 or MAT 132 (MAT 103 or MAT 128).
Textbooks:
1. Alan H. Kvanli
Introduction to business statistics. 1989.
2. Mario Triola
Elementary statistics. 2002.
3. Alan Hoenig
Applied finite mathematics. 1986.
4. Amir D. Azel
Complete Business Statistics. 1986.
5. Lawrence L. Lapin
Statistics for modern business. 1978.
6. С.К.Кыдыралиев, Б.М.Урмамбетов Сборник задач
статистике.2006.
по
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Method of Evaluating Outcomes: Grading
Tests are graded by a team of faculty from the Mathematics and Natural Sciences
Department. To ensure consistency each team member grades the same question(s) on each
test. Students may appeal the grading of a test question on a designated appeal day (time and
room to be announced). Students may discuss any problem with the faculty member who
graded their work and state the reason for the appeal. Only the grader determines whether
any adjustment to the grade should be made. Students should discuss the appeal with the
course instructor who will then make any necessary adjustment to the record and return the
paper to the department office. Grades will be based on a total of 100 points, coming from:
Quiz 1
The lecturer sets day and time
Midterm exam
March 9, 2014
Quiz 2
The lecturer sets day and time
Final Exam
May 4, 2014
Home works
Every class
The total grade of the student is as follows:
0  F  40  D  45  C-  50  C 60  C+ 65
65 B- 70  B  80  B+  85 A-  90  A 100.
современной
Objectives:
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to develop abstract and logical (probative) thinking,
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understanding how to set and solve problems,
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acquiring as basic knowledge of probability and statistical analysis techniques,
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to use the knowledge of probability and statistics for the problems solving in
majors.
10 points
30 points
10 points
40 points
10 points
Make-up Exams and Make-up Quizzes
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Expected outcomes:
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After completing MAT 313 the student will be able to:
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Use a general principle of counting, the multiplication principle, permutations,
combinations.
Understand the relationship between a question that arises in the natural, computer,
economic, and social sciences and the nature of the numerical data that are needed
in order to provide an answer to the question.
Formulate the question in a mathematical context, set up the required mathematical
procedure and carry out the required calculations, with appropriate use of a
calculator, to answer the questions.
Understand various types of descriptive measures, measures of dispersion,
interpreting sample mean and sample standard deviation.
Understand discrete probability distributions and continuous probability
distributions.
Understand hypothesis testing for the mean and variance of a population.
Draw a valid inference from a collection of numerical data.
Understand arithmetic of events, distributive laws.
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If the reason for missing the midterm exam is valid, the student’s final exam will be
worth up to 60 points. In this case extra tasks will be included in the final test.
If the reason for missing the final test is valid, a student can apply for the grade of
“I”. If the reason for missing the final is not valid, a grade of 0 will be given.
If a student misses both exams, he/she will not be attested for the course.
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3-5 weeks
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Probability. Direct calculation of probability. The theorem of addition of probabilities.
Conditional probability. Independent events. [1]: Ch. 4.1-4.5, [3]: Ch. 6.2 - 6.4, [2]: Ch.
3.1-3.5.
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Theorem of multiplication probabilities. The formula of unconditional (complete)
probability. Bayes’ rule. [3]: Ch. 6.5, [2]: Ch. 3.4.
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Random variables. Representing probability distributions for discrete random variables.
Mean and variance of discrete random variables. Binomial Random variables. [1]: Ch.
5.1-5.4, [3]: Ch. 9.5, [2]: Ch. 4.1-4.5.
If a student has missed Quiz 1 or Quiz 2 for a valid reason, the student may take
Quiz at the time specified by the lecturer, but before Midterm and Final Exams
respectively.
Attendance Requirements
It is important to attend classes to master the materials in the course. Attendance affects
grades: student loses 1 point for every missing class.
Academic Honesty
The Mathematics and Natural Sciences Department has zero tolerance policy for cheating.
Students who have questions or concerns about academic honesty should ask their professors
or refer to the University Catalog for more information.
6-8 weeks
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The hypergeometric distribution. The Poisson distribution [1]: Ch. 5.5-5.6, [2]: Ch. 4.4.
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Continuous random variable. Normal random variable. Determining a probability for a
normal random variable. [1]: Ch. 6.1-6.5, [2]: Ch. 5.1-5.4, [3]: Ch. 9.4.
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Random sampling and distribution of sample mean. The central limit theorem. [1]:
Ch.7.1-7.2, [3]: Ch. 4.1-4.4, [2]: Ch. 5.6.
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Using the Binomial to approximate the hypergeometric. [1]: Ch. 5.5, [5]: Ch. 17.1.
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Poisson approximation to the Binomial. [1]: Ch. 5.6, [2]: Ch. 4.4.
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Normal approximation to the Binomial. [1]: Ch. 6.6, [2]: Ch. 5.5, [5]: 3.7, 7.5.
Workbooks
Each student must maintain a math workbook with a clear record of completed homework.
Workbooks will be assessed from time to time. Students should bring their workbooks to all
classes as they are necessary for their class work. Workbooks must be submitted for
assessment immediately upon request of the instructor or full credit for homework may not be
earned. The workbook must contain calculations completed by the student. Photo-copies of
answers will not be accepted nor will answers that have been copied from the back of the text
book or transcribed from the solution manual. We highly recommend working jointly with
your fellow students on homework problems.
Calculators
Students will be advised whether calculators are needed for specific assignments. Graphic
calculators may not be used during quizzes and exams.
9-11 weeks
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Confidence intervals for the mean of a normal population (  is known). [1]: Ch. 7.3,
[3]: Ch. 5.1-5.2.
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Selecting the necessary sample size. [1]: Ch. 7.4 -7.5, [2]: Ch. 7.1,7.2, [3]: Ch. 5.3.
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Hypothesis testing on the mean of a population: large sample. On tailed test for mean of
a population: large sample. Reporting testing results using a p-value. [1]: Ch. 8.1-8.3,
[4]: Ch. 6.1-6.3, 6.6-6.8, [2]: Ch. 6.3.
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Confidence intervals for the mean of a normal population (  is unknown). [1]: Ch. 7.4,
[3]: Ch. 5.3-5.4.
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Hypothesis testing on the mean of a normal population: small sample. [1]: Ch. 8.4, [4]:
Ch. 6.4.
Writing the quiz and test in pencil is prohibited.
During the quiz and test going out is not allowed.
Cell phones
We ask students to turn off their cell phones during math classes. Using the cell phone is
entirely prohibited during the exam and quiz.
Syllabus change
Instructors reserve the right to change or modify this syllabus as needed; any changes will be
announced in class.
12-15 weeks
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Comparing the means of two normal populations using paired samples [1]: Ch. 9.5, [2]:
Ch. 8.3, [3]: Ch. 7.1-7.2, [5]: Ch. 6.10.
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Estimation and confidence intervals for a population proportion. [1]: Ch. 10.1, [2]: Ch.
7.3, [3]: Ch. 5.4 -5.6, [5]: Ch. 5.1-5.2.
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Hypothesis testing for the population proportion [1]: Ch. 10.2, [2]: Ch. 6.5, [3]: Ch.
6.5,6.6, [5]: Ch. 5.3, 5.4.
10. Tentative Academic Calendar:
1-2 weeks
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Combinatorial analysis. Permutations, rearrangement, combinations. A principle of
multiplication (Counting rule). [1]: Ch. 4.6, [3]: Ch. 5.4-5.6, [2]: Ch. 3.6.
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Sets. Union and intersection. Space of events. Elementary events. Operations above
random events. [3]: Ch. 6.1, [2]: Ch. 3.2.
Out-of class assignments
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Distribution function of discrete random variables. [4]: Ch. 2.2, [5]: Ch. 6.4.
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Comparing two means using two large independent samples [1]: Ch. 9.2