Statistics
4710/7710 - Introduction to Mathematical Statistics
Instructor:
Marco A. R. Ferreira
Email:
ferreiram@missouri.edu
url: http://www.stat.missouri.edu/~ferreiram
Office:
Middlebush 209E
Class
times: Monday, Wednesday and Friday, 1:00 - 1:50pm
Office
hours: Monday and Wednesday from 2 - 3pm (or by appointment).
Required
text:
- Introduction
to Probability and Statistics: Principles and Applications for Engineering and
the Computing Sciences, by J. Susan
Milton and Jesse C. Arnold
- Workbook is required
Evaluation:
- Three midterm exams (Points each: 100.
Total points: 300)
o
First
midterm: February 15
o
Second
midterm: March 14
o
Third
midterm: Apr 18
- One comprehensive final exam (Total points:
150)
o
Final
exam: May 16
- Fifteen homework assignments (1 or 2 per week)
(Points each: 10. Total points:
150)
- For graduate students taking this class (STAT
7710), an additional final project (Total points: 100)
Important
notes:
i) Exams may only be taken
early or made-up in the event of a pre-approved absence. If you miss an exam without prior
approval you may be given a grade of zero. If you must miss an exam for an approved reason, please see
me as soon as possible to make arrangements. All approved reasons for missing an exam require that
documentation be presented in advance. For example, if you miss an exam for a
medical reason, a note from a physician is required. Travel is not an
acceptable reason to miss an exam.
ii)
Homework
assignments have to be turned in on time.
iii)
Homework
assignments are individual tasks. Any kind of sharing or copying of homework assignments will be dealt with
utmost severity.
Material
from "Introduction to Probability and
Statistics: Principles and Applications for Engineering and the Computing
Sciences, by J. Susan Milton and Jesse C. Arnold" to be covered:
1
Introduction to Probability and Counting
1.1
Interpreting Probabilities
1.2
Sample Spaces and Events
1.3
Permutations and Combinations
2
Some Probability Laws
2.1
Axioms of Probability
2.2
Conditional Probability
2.3
Independence and the Multiplication Rule
2.4
Bayes' Theorem
3
Discrete Distributions
3.1
Random Variables
3.2
Discrete Probablility Densities
3.3
Expectation and Distribution Parameters
3.4
Geometric Distribution and the Moment Generating Function
3.5
Binomial Distribution
3.7
Hypergeometric Distribution
3.8
Poisson Distribution
4
Continuous Distributions
4.1
Continuous Densities
4.2
Expectation and Distribution Parameters
4.3
Gamma Distribution
4.4
Normal Distribution
4.5
Normal Probability Rule
4.6
Normal Approximation to the Binomial Distribution
4.7
Weibull Distribution
5
Joint Distributions
5.1
Joint Densities and Independence
5.2
Expectation and Covariance
5.3
Correlation
5.4
Conditional densities
6
Descriptive Statistics
6.1
Random Sampling
6.2
Picturing the Distribution
6.3
Sample Statistics
6.4
Boxplots
7
Estimation
7.1
Point Estimation
7.2
The Method of Moments and Maximum Likelihood
7.3
Functions of Random Variables--Distribution of X
7.4
Interval Estimation and the Central Limit Theorem
8
Inferences on the Mean and Variance of a Distribution
8.1
Interval Estimation of Variability
8.2
Estimating the Mean and the Student-t Distribution
8.3
Hypothesis Testing
8.4
Significance Testing
8.5
Hypothesis and Significance Tests on the Mean
8.6
Hypothesis Tests on the Variance
9
Inferences on Proportions
9.1
Estimating Proportions
9.2
Testing Hypothesis on a Proportion
9.3
Comparing Two Proportions: Estimation
9.4
Comparing Two Proportions: Hypothesis Testing
10
Comparing Two Means and Two Variances
10.1
Point Estimation: Independent Samples
10.2
Comparing Variances: The F Distribution
10.3
Comparing Means: Variances Equal
10.4
Comparing Means: Variances Unequal
10.5
Comparing Means: Paired Data
11
Sample Linear Regression and Correlation
11.1
Model and Parameter Estimation
11.2
Properties of Least-Squares Estimators
11.3
Confidence Interval Estimation and Hypothesis Testing
11.6
Correlation