# Ma 404: Probability & Statistics I

Elementary combinatorial analysis, independence and dependence, distribution functions, moment-generating functions, random variables, central limit theorem, elementary point and interval estimation, and hypothesis testing. Required calculator: TI 89 or Nspire CAS. Prerequisite(s): Ma 202, Ma 299. 3 Credits.

### Fall 2022 Course Information

- Instructor: Melissa Gardenghi
- Course Syllabus

#### Computational Resources

Accessing R: see my faculty page

Calculator Resources

Connectivity Software: TI-89 or TI-Nspire

Stats: ANOVA for TI-89, ANOVA for Excel

#### Interesting Problems

Exam P Problems - K.Ostaszewski, YouTube

#### Daily Expectations for Effective/Efficient Study

You may study any way you wish; however, there are certain approaches that just work better and allow you to avoid massive test studying sessions.

- Before considering any homework problems, take 5-10 minutes to add the ideas from today’s lecture to your “map” of the content. Don’t use paragraphs or even complete sentences. Do NOT just copy words from the lecture or book. Rewrite the ideas in your own (maybe awkward) words. Relate current ideas to previous.
- Take 10-20 minutes and consider all the theory discussed that day. Answer the following questions:
- How will you learn this theory without resorting to memorization (this will NOT work)
- What general tools were used (that might be reused again)?
- How can I tell when I should use this “general” tool?

- As you consider the recommended homework, answer the following questions:
- Where does this problem fit into my “map”?
- What technique/process did I use to solve this problem?
- What about the problem made me use that technique? Aka how will I recognize this question on the test when it looks different?
- Can I explain in a step-by-step format how to solve all problems of that form (in my own words, no “math” language, just “English”)? Add these instructions to a study sheet.

- Prior to the next class period, take 5 minutes to look over whatever we are covering next.
- Identify the big idea of that section (and maybe take note of any new vocab that we’ll see).
- Try and anticipate how this idea will fit into the new material.

- Each week dedicate 30-60 minutes to reviewing the following:
- The theory covered that week (and previously).
- The processes you developed to solve the problems discussed that week (and previously).

- Take notes that are not destined for the landfill. What do you need to write down so that your future (forgetful/confused) self will immediately understand what you are currently understand?

#### Data Analysis Project

This project give students the opportunity to develop the following professional competencies:

Intro to R Assignment (not collected for a grade, an aide for learning how to run statistical analysis in R)

Benefits Data (can be used to learn to use R)

Big Picture - Statistical Analysis

**Resources for Writing/Communicating Data**

See the handout summarizing how to better communication data (Handout on Presenting Data Effectively) and some examples of both good, better, and bad charts (Examples of Charts). Both handouts are based on the book by Cole Knaflic and the graphics are taken directly from the book.

Students can access an online copy of *Storytelling with Data* by Knaflic through the Mack Library Resources.

**Communicating Inferential Stats Effectively**

APA Guidelines for citing statistics: the following are helpful sites, you are welcome to use others

Purdue Online Writing Lab

Illinois State University - Dr. Jeffrey Kahn

APA Notation Chart, Graham Hole, Research Skills 2012

Statistics Solutions

APA

#### Tentative Course Content and Recommended Homework Problems

The tentative plan for covering course content includes the following sections (in roughly the given order). Recommended problems from the book are provided for each chapter.

Unit 1: Data Analysis

Ch 3: Sections 1 - 4

# 4, 7, 9, 13, 15, 16, 17, 19, 21, 24, 25, 31, 33, 37, 39

Ch 4: Sections 1 - 3, 5, 4

# 2, 3, 7, 9, 11, 19, 21, 23, 30, 31, 32, 33, 37

Ch 8: includes ch 6, section 5 (background on the Normal), Sections 4 - 6 (very, very briefly), 1 - 2

# 3, 63, 66, 67, 69, 71, 73, 75, 79, 81

Ch 13: Sections 1, 2 - 8 (from a practical implementation perspective only)

# 19, 25-31, 33a, 42-44, 47-48, 53, 57-59, 61, 63, 67, 73, 75, 77, 84-86 (include English for every problem that needs it) ... Ch 13 HT Handout

Ch 11: Sections 1, 2 - 7 (from a practical implementation perspective)

# 20-23, 28-30, 32, 34-36, 38, 39, 43, 49-54 (include English for every problem)

Ch 15: Sections 1 - 2 (from a practical implementation perspective)

# 17, 19 (include English for every problem)

Ch 14: Sections 2, 6 (from a practical implementation perspective)

# 41, 43, 45 (include English for every problem)

Unit 2 Counting and Classical Probability

Ch 1: Sections 1 - 3

# 1-3, 8-10, 24-57 (for #24-57, you probably won't be able to work all the problems, but you will benefit greatly from making sure you work all the "different" kinds of problems and identifying which problems are the "same" even though they seem different)

Ch 2: Sections 1 - 8

#1a, 2, 3, 6, 7, 11, 15, 18, 19, 22 (assigned in class), 23-26, 30, 42, 43, 51-55, 59-66, 70, 71, 73, 75, 78, 80, 81, 85-87, 89, 91, 93, 99, 103, 105, 110 (for the "number" problems, you probably won't be able to work all the problems, but you will benefit greatly from making sure you work all the "different" kinds of problems and identifying which problems are the "same" even though they seem different)

Unit 3 Discrete and Continuous Distributions

Ch 5: Sections 1 - 7, possibly 8 - 9 also

prove all the things we can prove for all the distributions, 25, 32, 41, 44, 49, 52-54, 57, 59, 62-64, 66, 68-70, 75, 79, 80, 81, 83, 86 (don't use the statistical tables for any of the these, use the formulas and then also the calculator distributions)

Ch 6: Sections 1 - 2, 3 (focusing on the Exponential), 5, possibly 6

#1, 16, 24a, 31, 37, 50, 51, 54-57, 59, 63, 64, 66, 68, 71, 73, 78, 79