Download MATH 131 Probability

MATH 131 : Probability
Zartash Afzal Uzmi
Instructor’s Name:
Office No. & Email: 2129
[email protected]
Office Hours: TW 4pm-5pm
Course
Description
Quarter:
Autumn
Category:
Math 131 (4 Units)
Basic Probability Theory. Discrete and Continuous Random Variables. Functions of
Random Variables. Expectations. Joint Distributions. Moment generating functions.
Core/Elective
Core for all
Pre-requisites
Calculus I
Goals
2002 / 2003
Nooruddin Abbas Ali Shah
TA for the Course:
Course Code
(Units)
Year:




To acquire a mathematical understanding of Probability Theory.
Be familiar with discrete (e.g., Bernoulli and Binomial) and continuous (e.g., Uniform
and Normal) Probability distributions.
Be able to compute densities and expectations of transformations and sums of
random variables.
To understand the concept of sampling distributions.
Math 131 : PROBABILITY
TextBooks,
Programming
Environment,
etc.
Year:
2002 / 2003
Quarter:
Autumn
REQUIRED TEXT:
A first course in Probability by Sheldon Ross
Other References: Modern Elementary Statistics by John E. Freund.
Prentice / Hall International editions.
Lectures,
Tutorials &
Attendance
Policy
There will be 30 sessions –
 20 of 75 minutes each
 10 of 50 minutes each
Attendance is not required but strongly recommended since there will be frequent surprise
short in-class quizzes.
Grading
Homeworks
Quizzes
Mid-term Exam
Final Exam
10%
20%
30%
40%
Regrading
Deadlines
(after graded
item returned)
Homeworks
Quizzes
Mid-term Exam
Final Exam
(No exceptions)
2days
2days
5days
End of first week of winter quarter
Math 131 : PROBABILITY
Module
1
2
Topics
Permutations and Combinations
Multinomial Coefficients
Year:
2002 / 2003
Quarter:
Autumn
Sessions
Readings
6
Ch. 1
Events
Sample Space
Counting Sample Points
Probability of an Event
Axioms of Probability
Ch. 2
Conditional Probability
Independence
Bayes’ Rule
Ch. 3
Random Variables
Distribution Functions (cdf, pdf)
Discrete Random Variables
Expected Value of Discrete Random Variables
Variance
Examples of Discrete Random Variables
7
Ch. 4
Continuous Random Variables
Expectation and Variance
Uniform Random Variable
Normal Random Variable
Exponential Random Variable
Distribution of a Function of Random Variable
5
Ch. 5
Joint Distributions
Conditional Distributions
Order Statistics
4
Ch. 6
4
Covariance and Correlation
Conditional Expectation
Moment Generating Functions
4
Ch. 7
5
Limit Theorems
Markov Inequality
Chebyshev's Inequality
The Central Limit Theorem
3
Ch. 8
Mid-Term Examination
3