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.