The aim of this course is to provide Basic Concepts of Probability theory to understand the nature of decision making in different fields of life. In this course we also discussed the different laws of probability. This course also covers the concept of random variable and its types and further discussions is on discrete and continuous probability distributions and its properties and applications. This course enables how to apply these distribution on real life situations.

Learning Outcomes

A prime objective of the course is to introduce the students to the fundamentals of the probability theory and present techniques and basic results of the theory and illustrate these concepts with applications. The  course will also present the basic principles of the random variables and random processes.At the end of this course,the students are able to solve the real life problems by applying problem solving techniques.Apply suitable probability distribution to solve the given problem.

Contents

1. Finite probability spaces
2. Basic concept, probability and related frequency
3. Combination of events, examples,
4. Independence, random variables, expected value
5. Standard deviation and Chebyshev's inequality
6. Independence of random variables
7. Multiplicatively of the expected value
8. Additivity of the variance
9. Discrete probability distribution.Probability as a continuous set function
10. Sigma-algebras, examples, continuous random variables,
11. Expectation and variance, normal random variables and continuous probability distribution.
12. Applications: De Moivre-Laplace limit theorem, weak and strong law of large numbers, the central limit theorem, Markov chains and continuous Markov process.

 Recommended Books :

1. Probability and Statistics for Engineers and Scientists by Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers and Keying E. Ye, Pearson; 9th Edition (January 6, 2011). ISBN-10: 0321629116
2. Probability and Statistics for Engineers and Scientists by Anthony J. Hayter, Duxbury Press; 3rd Edition (February 3, 2006), ISBN-10: 0495107573
3. Schaum's Outline of Probability and Statistics, by John Schiller, R. Alu Srinivasan and Murray Spiegel, McGraw-Hill; 3rd Edition (2008). ISBN-10: 0071544259.
4. Probability: A Very Short Introduction by John Haigh, Oxford University Press (2012). ISBN-10: 019958848

Suggested Books

1. Measure, Integral and probability, Springer-Verlag,1998.
2.  Basic probability Theory Dove. B, 2008.
3. Introduction to Statistical Theory Part I-II 8th ed.ilm kitab khana,lahore,Pakistan

ASSESSMENT CRITERIA

Assignment:          05

Presentation:         05

Attendance:          05

Quiz:                    05

Mid Exam:           30

Final exam:         50

KEY DATES AND TIME OF CLASS MEETING 

Monday (8-09:30 AM)

Friday ( 8-09:30 AM)

Commencement of Classses 

                 January 13,2020

Mid Term Examination 

                 March 09-13,2020

Final Term Examination 

                 May 04-08,2020

Declaration of Results 

                 May 19,2020