Download MATH 131 Probability

MATH 131 : Probability
Instructor’s Name:
Amjad Lone
Office No. & Email: 117-A
[email protected]
Office Hours: TBA
TA for the Course:
Course Code
(Units)
Course
Description
Year:
2002 / 2003
Quarter:
Summer
Category:
TBA
Math 131 (4 Units)
Basic Probability Theory. Discrete and Continuous Random Variables. Expected Value.
Functions of Random Variables. Joint Distributions. Moment Generating Functions. Central
Limit theorem and Law of Large Numbers.
Core/Elective
Core for all
Pre-requisites
Calculus I
Goals




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.
Be familiar with central limit theorem and law of large numbers.
Math 131 : PROBABILITY
Textbooks,
Year:
2002 / 2003
Quarter:
Summer
REQUIRED TEXT
Probability and Statistics for Engineers and Scientists by Walpole, R. Myers, and s. Myers,
Sixth edition, Prentice Hall International, Inc.
Reference Book
A first course in Probability by Sheldon Ross
4th edition, Macmillan Publishing Company
Lectures,
Tutorials &
Attendance
Policy
Grading
There will be 25 sessions of 80 minutes each
Attendance is not required but strongly recommended since there will be frequent surprise
short in-class quizzes.
Quizzes
Mid-term Exam
Final Exam
30%
30%
40%
1
Probability
Sample Space
Events
Counting Sample Points
Probability of an Event
Conditional probability
Multiplicative Rules
Bayes’ Rule
4
Ch. 2
2
Random variables and probability distributions
Random Variable
Discrete Probability Distributions
Continuous Probability Distributions
Empirical Distributions
Double Integration
Joint Probability Distribution
4
Ch. 3
3
Mathematical Expectation
5
Ch. 4
Expected Value of a Random Variable
Variance and Covariance
Mean and Variance Rules
Chebyshev’s Theorem
Mid-Term Exam
4
5
Discrete Probability Distributions
Introduction
Discrete Uniform distribution
Hypergeometric Distribution
Binomial distribution
Negative Binomial and Geometric Distribution
Poisson Distribution and the Poisson Process
3
Continuous Probability distribution
3
Ch. 5
Ch. 6
Continuous Probability distribution
Area Under the Normal Curve
Applications of the Normal Distribution
Normal approximation to binomial
Gamma and exponential distributions
6
Functions of Random Variables
Ch. 7
4
Introduction
Transformation of Variables
Moments and Moment Generating Functions
7
Limit Theorems
Sequence of Random Variables
The Weak Law of Large Numbers
The Central Limit Theorem
The Strong Law of Large Numbers
2
Ch. 8 of
reference
book