Silabus Probability Theory Jurusan Matematika Semester 5 / V

: Mathematics and Natural Sciences

Study Program           : Mathematics Education

Course & Code           : Probability Theory, MAA 318

Credit Hours               : Theory 2 credit, Practice 1 credit

Semester                     : V

Prerequisites & Code : Elementary Statistics, MAA 306

Lecturer                      : 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.   BASED 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 1-3 To understand the counting and combinatorial methods Combinatorial Methods: the basic principle of counting, permutation, combination Discussion & Exercises A: 31-39 B: 1-16 C: 1-113 4-6 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: 22-102 C: 1-113 7-10 To understand random variables and their properties, expectation, variance and moment generating functions Random Variables and Their Distributions: discrete random variables and continuous random variables Discussion & Exercises A: 53-83 B: 117-134 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: 134-224

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: 232-286
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: 297-373
27-32	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

IV. REFERENCES Compulsory textbooks  :

A.  Bain, Lee J. & Engelhardt, Max. 1992.  Introduction to Probability and Mathematical

Statistics. Belmont: Duxbury Press.

B.  Ross, Sheldon M. 2010. A First Course in Probability. New Jersey: Prentice-Hall.

Suggested reference books         :

C.  Rice, John A., 1995. Mathematical Statistics and Data Analysis. Belmont: Duxbury Press.

D.  Bluman, A.G. 2005. Probability Demystified. New York: McGraw-Hill.

V.   EVALUATION

No.	Components	Weight (%)
1.	Participations	10
2.	Assigment	10
3.	Quiz	15
4.	Mid Test	25
6.	Final Test	40
Total		100

Yogyakarta, September 2012

Verified by                                                                                         Lecturer

Head of Department

Dr. Hartono                                                                                         Rosita Kusumawati, M.Sc. 

NIP. 19620329 198702 1 002                                                             NIP. 19800707 200501 2 001