STAT 400: APPLIED PROBABILITY AND STATISTICS I

SECTION 0201, SUMMER II, 2020

COURSE OUTLINE

Instructor: Paul J. Smith, Statistics Program

E-mail: pjs@umd.edu

Schedule: Summer II, 2020, MTWTF 9:30-10:50, on line

Textbook: Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences (9th edition). Brooks/Cole.

Prerequisite: MATH 141 or MATH 131: Calculus II with minimum grade of C-, or permission of department.

Teaching format: Because of the COVID 19 pandemic, STAT 400 will be taught on line using ELMS and Zoom. We will meet virtually during the scheduled class time, I will upload class notes to ELMS and the sessions will be recorded on ELMS. During the scheduled class time, we will have two way video contact and live interaction. If you are unfamiliar with the technology, see the Keep Learning website here.

Course Description:

STAT 400 is the first semester of a calculus-based introductory course in probability and statistics. Probability is the mathematical treatment of random phenomena, and statistics is the science of collecting, analyzing and interpreting data subject to random variation. The course emphasizes applicable mathematics rather than abstract theory, and concepts will be illustrated using real-world examples wherever possible.
This course is not like the mathematics courses that you have taken in the past. Probability and statistics require a novel style of thinking and there will be a continual flow of new concepts and ideas. It is essential to stay current in the course and to work as many exercises as possible to master the material.
Because there are so many new ideas and concepts in STAT 400, it will not be possible to review techniques from algebra or calculus that are used extensively in the course. You must be proficient in algebra and calculus. Click here for a list of essential topics.

Topics:

Data summary and visualization: Graphical presentation of data, numerical data summaries of location and spread.

Probability: Sample space, events, probability axioms; relative frequency interpretation; equally likely outcomes; conditional probability and independence.

Discrete Random Variables: definitions; probability mass function and cumulative distribution function; expected values and moments; binomial, hypergeometric, geometric, Poisson distributions; applications.

Continuous Random Variables: densities: probability as an integral; cumulative distribution, expectation, moments, quantiles; uniform, exponential, normal distributions; applications.

Joint distributions and random sampling: bivariate random variables, joint and marginal distributions; expectation of functions of several random variables, correlation, covariance; independent random variables; mean and variance of sums of independent random variables, laws of expectation; Law of Large Numbers, Central Limit Theorem; distribution of a sample average.

Statistical inference: populations, statistics, parameters and sampling distributions; point estimators; criteria for accuracy; estimates of means, variances and proportions; confidence intervals for means and proportions, using confidence intervals to test hypotheses.

Examinations and Grading:

Midterms: There will be two midterms, on Friday, July 24 and on Friday, August 7. Exams will be given on line during the scheduled class period. Each midterm will count about 25% toward the final course grade.
Final exam: The final is scheduled for Friday, August 21, from 9:30 until 10:50. It will be comprehensive and will count about 40% toward the course grade.

Homework: You should be able to solve all problems in the textbook which deal with material covered in the course. Although some problems will be assigned as homework, collected and graded, you should not assume that solving only assigned problems will prepare you for tests. Homework will count about 10% toward the course grade and will not be accepted late. Click here for homework assignments.

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