Probability and Probability Distributions-I(STAT-305)

Objectives

Probability theory is the branch of mathematics that deals with modeling uncertainty. Probability distribution indicates the likelihood of an event or outcome. It is important because of its direct application in areas such as genetics, finance and telecommunications. It also forms the fundamental basis for many other areas in the mathematical sciences including statistics, modern optimization methods and risk modeling.This course is designed to establish conceptual framework ofhandling and understanding uncertain events probability and probability distributional approach, basic probability axioms and rules and the moments of discrete and continuous random variables as well as be familiar with commonly named discrete and continuous random variables

Learning Outcomes

This course enables the students to understand how to derive the probability density function of transformations of random variables and use these techniques to generate data from various distribution, how to calculate probabilities, and derive the marginal and conditional distribution of bivariate random variables. Methods on computations on Total probability theorem and Bayes theorem with implementation on the real life phenomenon are also provided. This course enables students how to derive distribution of functions of random variables by using the cumulative distribution function, transformation and m.g.f techniques.

Recommended Texts

1. Hogg, R. M. & Craig, A. T. (2013).Introduction to mathematical statistics (7 th ed.). New York: Prentice Hall.

2. Stuart, A. & Ord, J. K. (1998). Kendal’s advanced theory of mathematical statistics (1st ed.). London: Charles Coriffi and Co.

3. Mood, A. M, Graybill, F. A. & Boes, D. C. (1997). Introduction to the theory of Statistics. New York: McGraw Hill.

Sr No. Title
1 Week 1 Introduction to conditional probability and bayesian theorem
2 Week 2 Random Variable and its types
3 Week 3 Probability Mass Function and Probability Density function of random variable
4 Week 4 Marginal and Conditional Distributions
5 Week 5 Mathematical Expectation and its properties
6 Week 6 Moment generating function and Characteristic function of random variable
7 Week 7 Binomial Distribution and its properties
8 Week 8 Hypergeometric distribution and its properties
9 Week 9 Poisson Distribution and its properties
10 Week 10 Geometric distribution and its properties
11 Week 11 Negative Binomial distribution and its properties
12 Week 12 Multinomial distribution and its properties
13 Week 13 Uniform distribution and its properties
14 Week 14 Exponential distribution and its properties
15 Week 15 Gamma distribution and its properties
16 Week 16 Beta distribution and its properties

Assessment Criteria:

Exam:Mid(30%),Final(50%),

Sessional(20%):Assignment,Presentations,Class Participation,Quizzes

Time Table: BS-V Regular

Monday(10:00 AM to 11:00 AM)

Tuesday(09:00 A.M to 10:00 AM)

Wednesday (10:00 A.M to 11:00 A.M)

BS-Self Support

Monday(03:00 PM to 04:00 PM)

Tuesday(04:00 P.M to 05:00 PM)

Thursday (12:30 P.M to 01:30 PM)

 

 

Course Material

Other Courses by Sundus Haqqani