MATH 3215 Introduction to Probability and Statistics and
Applications
Spring 2014
TTr 9:30-11:00
Office Hours: TTr 3-4, 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:
R.V. Hoggs and E.A. Tanis "Probability ans Statistical Inference",
8th edition
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.
First Midterm: February
18 Second Midterm: March
25
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
- Point Estimation
- Statistical Intervals
- Test of Hypotheses
- Simple Linear Regression (time permitting)
First week
Material covered:
- General Introduction
- 1.1 Basic Concepts
- 1.2 Properties of Probability
Exercises:
- (1.1) 2, 7
- (1.2) 6, 15, 19
Second week
Material covered:
- 1.3 Methods of Enumeration
- 1.4 Conditional Probability
- 1.5 Independent Events
Exercises:
- (1.3) 7, 11
- (1.4) 1, 10, 15
- (1.5) 3, 18, 19
First HW collection on Tuesday January 21nd.
Third week
Material covered:
- 1.6 Bayes's Theorem
- 2.1 Random Variable of Discrete Type
Exercises:
- (1.6) 4, 8, 11
- (2.1) 3, 7, 17
Fourth week
Material covered:
- 2.2 Mathematical Expectation
- 2.3 The Mean, Variance and Standard Devioayion
- 2.4 Bernoulli Trials and the Binomial Distribution
Exercises:
- (2.2) 5, 12
- (2.3) 5, 13, 19
- (2.4) 7, 22
Second HW collection on Thursday February 6th.
Fifth week
Material covered:
- 2.5 The Moment-Generating Function
- 2.6 The Poisson Distribution
Exercises:
- (2.5) 3, 11, 21
- (2.6) 13, 15, 21
Seventh week
Material covered:
- 3.1 Continuous-Type Data
- 3.2 Exploratory Data Analysis
Exercises:
- (3.1) 3, 10, 12
- (3.2) 4, 9
The first midterm will be on
Tuesday February 25. It will cover Chapter 1 and 2 complete plus
section 3.1 and 3.2 from the book.
Preparation Material
Solution set
for the first midter.
Third HW collection on Teusday March 11th.
Eighth week
Material covered:
- 3.3 Random Variable of Continuous Type
- 3.4 The Uniform and Exponential Distribution
Exercises:
- (3.3) 2, 7, 23
- (3.4) 5, 6, 14, 20
Nineth week
Material covered:
- 3.5 The Gamma and Chi-square Distributions
- 3.6 The Normal Distribution
Exercises:
- (3.5) 8, 11
- (3.6) 5, 7, 14, 25
Tenth week
Material covered:
- 4.1 Distributions of 2 Random Variables
- 4.2 The Correlation Coefficient
- 4.3 Conditional Distributions
- 4.4 The Bivariate Normal Distribution
Exercises:
- (4.1) 5, 12, 15
- (4.2) 1, 7, 10
- (4.3) 6. 16
- (4.4) 8
Fourth HW collection on Teusday April
1st.
Preparation material for the second
midterm:
Solution set
for the second midter.
Eleventh week
Material covered:
- 5.1 Functions of One Random Variable
- 5.3 Several Independent Random Variables
- 5.6 The Central Limit Theorem
Exercises:
- (5.1) 6, 8
- (5.3) 6, 11, 22
- (5.6) 7, 8, 12
Twelfth week
Material covered:
- 6.1 Point Estimation
- 6.2 Confidence Interval for the Mean
Exercises:
- (6.1) 5, 13, 15
- (6.2) 5, 10, 14
Last HW collection on Thursday April
17.
Take home midterm due on April 22.