Faculty                                   : Mathematics and Natural Sciences
Study Program                       : Mathematics Education
Course & Code                       : Probability Theory, MAA 317
Credit Hours                           : Theory 2 credit, Practice 1 credit
Semester                                 : IV
Prerequisites & Code             : Elementary Statistics, MAA 306
Lecture                                   : Kismiantini, M.Si.

I.    COURSE DESCRIPTION

The course is more focused on probability concepts than statistical mathematics. The materials of probability theory are combinatorial methods, probability, random variables and their distributions, joint distributions, properties of random variables, and functions of random variables.

II.  BASIC COMPETENCY

The students able to use probability and probability distribution for solving a real problem and mathematics problem which is need the calculation of probability, prove the theorems which related to probability, and find a relationship between distributions, and determine expected value of random variables.

III. ACTIVITIES PLAN 

Meeting
Based Competency
Subject Matter
Activities
References



1-2
To understand the counting and combinatorial methods
Combinatorial Methods: the basic principle of counting, permutation, combination
Discussion & Exercises
A: 31-39
B: 1-16





3-5
To understand the
axiomatic approach to probability, some properties of probability, conditional probability and Bayes theorem
Probability: definition of
probability, some properties of probability, conditional probability, Bayes theorem
Discussion &
Exercises
A: 1-30
B: 25-54

6-10
To understand
random variables and their properties,
Random Variables and Their
Distributions: discrete random variables and continuous
Discussion &
Exercises
A: 53-83

expectation,
variance and moment generating functions
random variables


11

Test I






12-16
To recognize and
learn the special probability distributions and their properties distributions
Special Probability
Distributions: special discrete distributions and special continuous distributions
Discussion &
Exercises
A: 91-124
B: 126-232



17-21
To solve a
probability problem with reference to joint distributions
Joint Distributions: joint
discrete distributions, joint continuous distributions, independent random variables, and conditional distributions
Discussion &
Exercises
A: 137-160
B: 244-293
22

Test II








23-26
To explain some properties of random variables such as expected values, covariance, correlation,
conditional
expectation, and joint moment generating functions
Properties of Random Variables: properties of expected values, covariance, correlation, conditional expectation, joint moment generating functions
Discussion & Exercises
A: 171-188
B: 309-372






27-31
To gain the ability to use some properties of random variables and their distribution in
functions of random variables
Functions of Random Variables: the cumulative density function technique, transformation methods, joint transformations, sums of random variables, moment generating function method
Discussion & Exercises
A: 193-214
32

Final Test


IV. REFERENCES

A.  Compulsory textbooks         :
Bain, Lee J. & Engelhardt, Max. 1992. Introduction to Probability and Mathematical
Statistics. Belmont: Duxbury Press.

B.  Suggested reference books  :
Ross, Sheldon M. 1998. A First Course in Probability. New Jersey: Prentice-Hall.

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