MATH 3670 Probability and Statistics with Applications
Spring 2017
MWF 9:05-9:55, College of Computing 17
Office Hours: MWF 11:00-12:00, Skiles 133b
The course will introduce the basic notion of probability theory and
its application to statistics. The focus will be on the discussion of
applications.
The text that will be used is:
Jay L. Devore, Probability and Statistics,
8th or 9th ed., Thomson
The syllabus can be found here.
There will be two midterm.
The exercise listed are for HW collection. I will collect them
every
two weeks and grade 2 or 3 exercises among the one assigned. In case of
differences between the 9th and 8th editions of the book I will
indicate in square brackets the number relative to the 8th edition.
The final grade will be based on the following rules: 40%
final, 40%
midterms,20% HW. Curving will be done on the final result.
The first midterm will be on Friday February 17 and the
second on Friday March 31.
Arguments covered.
- Axioms, Interpretations and Properties of Probabilities
- Probability Distributions for Discrete Random Variables
- Example of Discrete Random Variables
- Continuous Random Variables and Probability Density
Functions
- Example of Continuous Random Variables
- The central limit theorem
- Jointly Distributed Random Variables
- Population, Sample and Processes
- Point Estimation
- Statistical Intervals
- Test of Hypotheses
- Simple Linear Regression (time permitting)
See the webpage
of the Spring 2016 class for previous tests and material.
First week
Material covered:
- 1.1 (Population, Sample and Processes)
- 1.2 (Pictorial and Tabular methods in Descriptive Statistics)
- 1.3 (Measure of Location)
- 1.4 (Measure of Variability)
Exercises:
- (1.3) 34, 38
- (1.4) 49, 51
Second week
Material covered:
- 2.1 (Sample Spaces and Events)
- 2.2 (Axioms, Interpretations and Properties of Probabilities)
Exercises:
- (2.1) 3, 5, 9
- (2.2) 13, 21
First HW due on January 25.
Third week
Material covered:
- 2.3 (Counting Technique)
- 2.4 (Conditional Probability)
Exercises:
- (2.3) 32, 40
- (2.4) 50, 58, 63
Fourth week
Material covered:
- 2.5 (Indipendence)
- 3.1 (Random Variables)
- 3.2 (Probability Distributions for Discrete Random Variables)
- 3.3 (Expected Values of Discrete Random Variable)
Exercises:
- (2.5) 80, 87
- (3.1) 6, 8, 10
- (3.2) 16, 23, 27
- (3.3) 29, 35 39, 42
Second HW due on February 8
Fifth week
Material covered:
- 3.4 (The Binomial Probability Distribution)
- 3.5 (Hypergeometric Distribution)
Exercises:
- (3.4) 49, 54 63, 65
- (3.5) 70, 72
The first midterm will be on February 17. The midterm will cover the material up to section 3.6.
Preparation material for the first midterm:
Solution set for the first midterm.
Sixth and seventh weeks
Material covered:
- 3.6 (The Poisson Probability Distribution)
- 4.1 (Continuous Random Variables and Probability Density Functions)
- 4.2 (Cumulative Distribution Functions and Expected Values)
- 4.3 (The Normal Distribution)
- 4.4 (The Exponential Distribution)
Exercises:
- (3.6) 85, 89
- (4.1) 2, 5, 8
- (4.2) 11, 25
- (4.3) 28, 29, 31, 41
- (4.4) 59, 69
Third HW due on March 10.
Eighth week
Material covered:
- 5.1 (Jointly Distributed Random Variables)
- 5.2 (Expected Values,Covariance and Correlation)
- 5.5 (The Distribution of a Linear Combination)
Exercises
- (5.1) 1, 8, 15, 17
- (5.2) 22, 25, 30
- (5.5) 59, 64, 68
Nineth week
Material covered:
- 5.3 (Statistics and their distribution)
- 5.4 (The Distribution of the Sample Mean)
Exercises:
- (5.3) 37, 41, 42
- (5.4) 48, 49, 53, 56
The second midterm will
be on Friday 3/31. It will cover all the material up to Chapter 5 included.
You may use a scientific calculator but no laptop or calculator able to
do symbolic differentiation or integration. No cheat sheet will be
allowed.
Preparation material for the second midterm: