Download MATH 230- Probability

Lahore University of Management Sciences
BSc (Hon) Programme
Course Outline
Muhammad Ismail
Course Code:
Course Title:
Pre–requisite:
Semester:
Credits:
Math 230
Probability
Math 102 (Calculus - II)
Spring 2008 – 2009
three (03)
Course Description:
The use of probability concepts is almost evident in all the areas of life. An understanding of
probability concepts is essential for students who want to pursue their studies in Basic and
Management Sciences. The knowledge of probability concepts with rigorous study of probability
distributions is mandatory for decision making in all the areas of sciences.
This course covers basic probability concepts and probability distributions useful for decision
making in Management and Engineering Sciences. The course starts with introduction of
probability terms and methods of computing simple and conditional probabilities. The Baye’s
theorem will be taught with applications. The concept of discrete and continuous random variables
will be given. Bivariate random variables will be explored with marginal and conditional
distributions. The expectation and variance of random variables will be studied. Covariance and
correlations of random variables will be discussed. Special discrete and continuous probability
distributions will be explored with their real life applications. Moments and moment generating
function will be discussed. Moments of special discrete and continuous probability distributions will
be examined.
Goals
At the end of the course the student should be able to do the following
 Compute simple and conditional probabilities in different situations
 Efficiently use the concept of random variables
 Apply suitable distribution in solving real life problems
Evaluation
 Quizzes
 Home Assignments
 Mid – term
 Final Exam
12
02
01
01
25 Marks (10 best will be considered)
10 Marks
25 Marks
40 Marks
Text Book
 Probability and Statistics for Engineers and Scientists, 8th Edition by Walpole, Myers and Ye
Week wise Schedule of MATH–231 (Probability)
Week
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Topics
 Introduction to Probability
 Random Experiment, Sample Spaces and Events
 Rules of Counting including Permutations and Combinations
 Probability of an Event, Simple and Compound Probabilities
 Addition Law of Probability for two and three events
 Conditional Probability and Multiplication Law of Probability
 Baye’s Law and its application
 Introduction to Random Variables
 Discrete Random Variable and its Probability Distribution
 Continuous Random Variable and its Density Function
 Distribution Function and its Use
 Joint Discrete and Continuous Distributions
 Conditional and Marginal Probability Distributions
 Expectation and Variance of a Random Variable
 Expectation and Variance of Function of Random Variables
 Joint Expectation and Covariance of Two Random Variables
 Mean and Variance of Linear Combination of Random Variables
Mid Term
 The Chebyshev’s Theorem
 Special Discrete Distributions: Uniform, Binomial, Multinomial, Hypergeometric
 Special Discrete Distributions (Continued): Negative Binomial and Poisson
Distributions
 The Continuous Uniform, Exponential and Gamma Distributions with applications
 The Normal Distribution and its use
 The Weibull and Lognormal Distributions with applications
 Functions of Random Variable
 Moments of Random Variables
 Moment of Special Discrete Distributions
 Moments for Special Continuous Distributions
 Moment Generating Function and its use
 Sampling Distributions of mean