Approved by University Studies Sub-Committee.  A2C2 action pending.

University Studies Course Approval Proposal

 

Flagged Courses Writing

 

 

The Department of Mathematics and Statistics proposes the following course for inclusion in University Studies, Flagged Courses, Mathematics and Statistics at Winona State University.  This was approved by the full department on Thursday, January 18, 2001.

 

 

Course: Introduction to Mathematical Statistics I (STAT 450), 3 S.H.

 

Catalog Description: A mathematical approach to probability and statistics.  Prerequisite:   MATH 260 and completion or concurrent enrollment in MATH 220.

 

Department Contact Person for this course:

      Christopher J. Malone

      Department of Mathematics and Statistics

      Email:  cmalone@winona.edu

 

Comment:  This is the first course of a two-semester sequence that is a requirement for a major in statistics.   A writing flag proposal for the second course, Introduction to Mathematical Statistics II (STAT 460), is being submitted separately.  

 

 

Writing Flag

 

The purpose of the Writing Flag requirement is to reinforce the outcomes specified for the basic skills area of writing. These courses are intended to provide contexts, opportunities, and feedback for students writing with discipline-specific texts, tools, and strategies. These courses should emphasize writing as essential to academic learning and intellectual development.

 

Courses can merit the Writing Flag by demonstrating that section enrollment will allow for clear guidance, criteria, and feedback for the writing assignments; that the course will require a significant amount of writing to be distributed throughout the semester; that writing will comprise a significant portion of the students’ final course grade; and that students will have opportunities to incorporate readers’ critiques of their writing.

 

 


The writing flag requirement in relation to STAT 450 

 

… to reinforce the outcome for the basic skills area of writing

 

An important writing skill for a student of statistics is that of summarizing the general strategy of a result or derivation in a non-rigorous fashion.  In particular, a student within the field of statistics must be able to communicate complex derivations to non-statisticians.  A student will receive several opportunities to engage in such writing throughout the semester.  In each case, the student will receive feedback on the appropriateness their writing style.

 

... to provide contexts, opportunities, and feedback for students writing with discipline-specific texts, tools, and strategies

 

In addition to summarizing a general strategy in a non-rigorous fashion, a student is frequently asked to engage in discipline-specific writing commonly found in mathematical statistics.  The discipline-specific writings often involve rigorous proofs of various theorems, lemmas, and corollaries.  Such writings require a student to go beyond the basic understanding of some previously discussed concept.   The student will receive feedback on the appropriateness of their writing style.  However, unlike the non-rigorous writings, these writings are more technical in nature and may be understandable only to a mathematical statistician.

 

 

The types of writing discussed above require the student to extend their basic understanding of a particular concept.  The student is asked repeatedly to convey complex concepts in a precisely written format. 

 

 


Details to how STAT 450 satisfies the writing flag requirements  

 

Writing Flag courses must include requirements and learning activities that promote students’ abilities to:

 

a.      practice the processes and procedures for creating and completing successful writing in their fields

 

This course is the first of a two-semester sequence in which a rigorous introduction to theoretical statistics is established.  To successfully complete this course, a student is required to demonstrate not only an understanding of the concepts involved in a derivation, but also an ability to convey those concepts in concisely written form.  The student is asked to communicate concepts in a non-rigorous writing style with the intent of being understood by the lay-person.  In addition to these non-rigorous writings, proof writing techniques are communicated and these writings are most likely accessible only to mathematical statisticians.    These writing styles require a complete understanding of the concepts involved, knowledge of good grammatical structure, and knowledge of good sentence structure.   The student will receive several opportunities to engage in these writing styles throughout the semester.  In each case, the student will receive significant feedback on the appropriateness of their writing style.

 

 

b.      understand the main features and uses of writing in their fields

 

A student of statistics must be able to communicate concepts to a non-practitioner of statistics, as well as articulate their understanding of a difficult concept to an individual with significant training in mathematical statistics.  The material covered in this course naturally allows the student to participate in commonly found writing styles found within the field of Statistics.   The instructor will spend a great deal of time discussing the technical correctness and appropriateness of the different writing styles.

 

 

c.      adapt their writing to the general expectations of readers in their fields

 

As previously mentioned, the student will receive ample opportunities to engage in various writing styles throughout this required course sequence.   Upon getting continual feedback form the instructor as the semester progresses, the student’s ability to write effectively should improve and eventually be well-aligned with common expectations within the field of Statistics.

 

 

 

 


d.      make use of technologies commonly used for research and writing in their fields

This course introduces students to theoretical statistics and so the use of software packages is somewhat limited.  However, several statistical concepts taught in this course can be elaborated upon through the use of statistical software packages.  These elaborations are left to the discretion of the instructor.  In addition to statistical software packages, students should be exposed to equation editors which are commonly found in word processing packages.

 

e.      learn the conventions of evidence, format, usage, and documentations in their fields

 

The usage of language and formatting issues is considerable different when writing to a non-statistician versus an individual with considerable training in mathematical statistics.  The instructor will address such issues and provide feedback to the students as needed.

 

 

 

 


Writing flag requirements in relation to the course outline

 

Writing Flag:

 

Writing flag courses must include requirements and learning activities that promote students' abilities to...

 

a.      practice the processes and procedures for creating and completing successful writing in their fields;

b.      understand the main features and uses of writing in their fields;

c.      adapt their writing to the general expectations of readers in their fields;

d.      make use of the technologies commonly used for research and writing in their fields; and

e.      learn the conventions of evidence, format, usage, and documentation in their fields.

 

Outline of Topics:

 

      A. Probability (a),(b),(c),(d),(e)

      B. Random Variables (a),(b),(c),(d),(e)

      C. Distribution and Density Functions (a),(b),(c),(d),(e)

      D. Expectation and Moments (a),(b),(c),(d),(e)

      E. Parametric Families of Univariate Distributions including Uniform, Bernoulli,

           Binomial, Hypergeometric, Poisson, Geometric, Negative Binomial, Normal,

           Exponential, Gamma, and Beta distributions (a),(b),(c),(d),(e)

      F. Joint Distributions including covariance and correlation (a),(b),(c),(d),(e)

      G. Conditional Distributions (a),(b),(c),(d),(e)

      H. Stochastic Independence (a),(b),(c),(d),(e)

I.        Expectations of Functions of Random Variables (a),(b),(c),(d),(e)

J.       Cumulative Distribution Functions (a),(b),(c),(d),(e)

K.     Moment Generating Functions (a),(b),(c),(d),(e)

L.      Transformations (a),(b),(c),(d),(e)

Additional topics as time permits

 

Basic instructional Plan: The basic methods of instruction will be lecture and discussion.

 

Course requirements and means of evaluation: Possible methods include homework problems (a),(b),(c),(d),(e), examinations (a),(b),(c),(e), quizzes, and/or a final examination (a),(b),(c),(d),(e)

 

Possible textbooks:

         Casella, George & Berger, Roger.  Statistical Inference.  Wadsworth/Brooks-Cole, 1990.

         Bain, Lee J. & Engelhardt, Max.  Introduction to Probability and Mathematical Statistics.  PWS-KENT, 1992.

         Hogg, Robert V. & Craig, Allen T.  Introduction to Mathematical Statistics (Fifth Edition).Prentice Hall, 1995

         Larsen, Richard J. & Marx, Morris L.  An Introduction to Mathematical Statistics and its Applications (Third Edition).    Prentice Hall, 2001.

 

 


Two Examples:

 

In accordance with criteria a., b., c., d., and e., this course requires the student to write using writing styles commonly found within the field of Statistics.  A student may be asked to discuss a general strategy or derivation to a non-statistician.  On the other hand, a student may be asked to provide a rigorous proof of a concept that may be accessible only to a mathematical statistician.  Two examples are provided here.  The first is an example of non-rigorous writing and the second is an example of the technical writing required in a proof. 

 

 

Example 1:  The Empirical rule and Chebychev’s rule are used to determine a range of likely values for a particular distribution.  Discuss any differences between these rules so that a common lay-person would understand.

 

The main distinction between these rules is that Empirical rule requires that the observations come from a bell-shaped distribution; whereas, Chebychev’s rule applies to a distribution of any shape.  Chebychev’s rule is conservative when applied to bell-shaped distributions because the range of likely values is larger than those obtained using the Empirical rule.  If the shape of the distribution is unknown, then Chebychev’s rule should be used to safe guard against a liberal range of likely values.

 

 

Example 2:  We’ve discussed and utilized Jensen’s Inequality several times in class.    Prove this inequality.

 

 

Claim:  For any random variable, if  is a convex function, then

 

.

 

Proof:

To establish the inequality, let  be a tangent line to  at the point .  Recall that is a constant.  Write  for some and .  This situation is illustrated in the following figure.

 

By the convexity ofwe have .  Since expectations preserve inequalities,

 

 

which is what was to be shown.