MATH 3770 Statistics and Applications
Fall 2011
MW4:35-5:55 Skiles 249
Office Hours: MW 11-12, 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 7th 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 8th and 7th editions of the book I will
indicate in square brackets the number relative to the 7th edition.
The final grade will be based on the following rules: 45%
final, 35%
midterms, 20% HW. Curving will be done on the final result.
Arguments covered.
- Population, Sample and Processes
- 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
- Point Estimation
- Statistical Intervals
- Test of Hypotheses
- Simple Linear Regression (time permitting)
See the webpage
of the spring 2010 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:
- (1.1) 3, 7
- (1.2) 17, 19, 25, 27
- (1.3) 35, 39, 41
- (1.4) 45, 49, 51, 59
Second week
Material covered:
- 2.1 (Sample Spaces and Events)
- 2.2 (Axioms, Interpretations and Properties of
Probabilities)
- 2.3 (Counting Technique)
Exercises (the numbers in square brackets refer to the 6th edition of
the textbook):
- (2.1) 3, 5, 9
- (2.2) 13, 17, 21
- (2.3) 32, 36, 40
Fisrt HW due on
Wednesday 7 September
Third week
Material covered:
- 2.4 (Conditional Probability)
- 2.5 (Indipendence)
Exercises (the numbers in square brackets refer to the 7th edition of the textbook):
- (2.4) 50, 58, 63
- (2.5) 80 [78], 84 [82], 87 [85]
Fourth week
Material covered:
- 3.1 (Random Variables)
- 3.2 (Probability Distributions for Discrete Random Variables)
- 3.3 (Expected Values of Discrete Random Variable)
- 3.4 (The Binomial Probability Distribution)
Exercises (the numbers in square brackets refer to the 6th edition of the textbook):
- (3.1) 6, 8, 10
- (3.2) 12, 16, 19 [20], 23 [22], 27 [26]
- (3.3) 29 [28], 35 [34], 37 [36], 38 [37], 42 [41]
- (3.4) 48 [46], 54 [50], 58 [54], 63 [59], 65 [61]
Second HW due on Wednesday 21 September
Fifth week
Material covered:
- 3.5 (Hypergeometric Distribution)
- 3.6 (The Poisson Probability Distribution)
- 4.1 (Continuous Random Variables and Probability Density Functions)
- 4.2 (Cumulative Distribution Functions and Expected Values)
Exercises:
- (3.5) 69, 70, 72
- (3.6) 85, 88, 89, 92
- (4.1) 2, 5, 8
- (4.2) 11, 17, 22, 25
Sixth week
Material covered:
- 4.3 (The Normal Distribution)
- 4.4 (The Exponential Distribution)
Exercises:
-
(4.3) 28, 29, 31, 35, 41, 46
- (4.4) 59, 69
The first midterm will be on October 5th.
Preparation material for the first midterm:
Third HW due on Wednesday 12 October
Seventh 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, 12, 15, 17
- (5.2) 22, 25, 27, 30
- (5.5) 58, 59, 64, 68, 73
Eigth week
Material covered:
- 4.6 (Probability Plots)
- 5.3 (Statistics and their distribution)
- 5.4 (The Distribution of the Sample Mean)
Exercises: - (4.6) 87, 88
- (5.3) 37, 40, 41, 42
- (5.4) 46, 49, 51, 53, 56
Fourth HW due on Wednesday 2 November
The second midterm will
be on Monday 11/7. It will cover all the material up to Chapter 6 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:
Nineth week
Material covered:
- 6.1 (Some General Concepts of Point Estimation)
- 6.2 (Methods of Point Estimation)
Exercises:
- (6.1) 1, 5, 7, 11, 19
- (6.2) 22, 23, 25, 30
Tenth week
Material covered:
- 12.1 (The Simple Linear Regression Model)
- 12.2 (Estimating Model Parameter)
Exercises:
- (12.1) 3, 7, 9
- (12.2) 12, 16, 21, 24
Fifth HW due on Wednesday 30 November
Tenth week
Material covered:
- 7.1 (Basic Properties of Confidence Intervals)
Exercises:
- (6.2) 20, 22, 23, 25, 29, 30
- (7.1) 1, 2, 4, 5, 8, 11
Eleventh week
Material covered:
- 7.1 (Basic Properties of Confidence Intervals)
- 7.2 (Large Sample Confidence Interval for the Population Mean and Proportion)
- 7.3 (Interval Based on a Normal Population Distribution)
Exercises:
- (7.1) 1, 2, 4, 5, 8, 11
- (7.2) 12, 15, 18, 24, 26
- (7.3) 28, 29, 32, 38
Twelfth week
Material covered:
- 8.1 (Hypotheses and Test Procedures)
- 8.2 (Tests about a Population Mean)
- 8.4 (P-values)
Exercises:
- (8.1) 3, 5, 8, 11
- (8.2) 15, 19, 23, 25, 26
- (8.4) 46, 54, 56
Solution set for the midterms: midterm 1 and midterm 2
Preparation material for the final. Here is a link to collected previous term exams with some solutions.