New HampshireTechnicalCollegeNashua
505 Amherst Street
NashuaNH03063
September, 2005
PROBABILITY AND STATISTICS
Curriculum and Course Number: MATHEMATICS - MTHN217
Department: Mathematics
Credit Hours: 4
Semester Hours: Class 4
Prerequisite: MTHN210, Prerequisite or Co requisite: MTHN211
COURSE DESCRIPTION
This course begins with a discussion of the differences between descriptive and inferential statistics, the different types of data, and the rudiments of statistical distributions. Classical probability theory and probability distributions are discussed in general. Specific probability distributions appropriate to discrete data and continuous data are developed in detail. Estimation, hypothesis testing, and applications provide "real life" examples. Linear relationships and regression analysis provide another means to make predictions and show correlations.
Course Competencies:
At the successful completion of this course the student will be able to:
- Understand basic techniques to characterize statistical data.
- Understand and apply basic probability theory.
- Understand the probabilistic basis of inference.
- Understand the properties of specific probability distributions of discrete random variables.
- Understand the properties of specific probability distributions of continuous random variables.
- Understand the utility of and use moment generating functions.
- Calculate expected values.
- Apply standard parameters to describe statistical distributions
- Apply the basic of multivariate probability rules.
- Perform estimations and determine the reliability of those estimates.
- Create hypotheses and apply standard tests to those hypotheses
- Understand linear modeling and use regression analysis.
Course Outline:
- Introduction to Statistics
- Define the discipline
- Characterizing data graphically
- Area under a distribution
- Distribution shapes.
- Characterizing data numerically
- Measures of central tendency
- Variance, standard deviation, empirical rule
- Concept of inference
- Compare/contrast mathematical models with chance outcomes
II. Basics of Probability Theory
A. Inference and its roots in probability.
- Set theory, events, sample spaces
- Factorial and counting rules
- Conditional probability
- Probability rules
- Mutually exclusive events
- Logical joiners
- Additive rule
- Independent events
- Multiplicative rule
- Event composition method
- Complementarity
- Bayes' rule
F. Random Variables
III.Discrete Random Variables
- Definition
- Binomial probability distribution
- Geometric probability distribution
- Poisson probability distribution
- Expectation values
- Moment generating function
- Chebychev's theorem
IV. Continuous Random Variables
- Devinition
- Probability density function
- Uniform probability distribution
- Normal probability distribution
i.z scores
- relative standing
- Beta function distribution
- Expectation values
IV.Multivariate probability distributions
A.Contingency tables
i.. Marginal probability
ii. Conditional probability
iii. Independence
B. Covariance of 2 random variables
V.Estimation in Statistics
- Samples versus populations
- Random Sampling
- Properties of estimators
i. Point estimators
ii. Evaluating the estimator
D. Confidence intervals
i. Selecting the sample size
ii. Large samples
iii. Small samples
E. Methods of estimation
i. Method of moments
ii. Methods of maximum likelihood
VI.Hypothesis testing
- Elements of a statistical test
- Z test
- t test
- Linear Regression
- Linear modeling
- Estimation/prediction
- Method of least squares
- Correlation and correlation coefficient
- Error analysis
Learning/Instructional Methods:
1. Lecture and Discussion
2. Illustrations and Examples
3. Problem Solving
Performance Evaluation:
1. Quizzes
2. Tests
3. Assignments
4. Midterm and Final Comprehensive Examinations
Suggested Text:
DeGroot, Morris H & Schervish, Mark J; Probability and Statistics, 3rd Edition, Addison-Wesley, 2002
Date outline developed: April, 2002
Dates of Revision: September, 2002
September 2005 – Textbook and numbering change