Math 526: Applied Mathematical Statistics I

MATH 526: A first course in statistics for students with the techniques of calculus at their disposal. The following topics will be studied with illustrations and problems drawn from various fields of applications: basic notions of probability and probability distributions; classical estimation and testing procedures for one and two sample problems; chi-square test.

The course will be comprised of a series of "mini-units" focusing on fundamental topics in mathematical statistics:
1. Probability Distributions, 2. Data Analysis and Estimation, 3. Testing Hypotheses, 4. Regression Analysis.

Professor: Bozenna Pasik-Duncan
Telephone: (785) 864-5162
Email: bozenna@ku.edu

Office: 503 Snow Hall
Office Hours: TR 9:30-10:30 a.m.



Announcements

  • New Announcement Final Exam
    The Final Exam is scheduled for Wednesday, December 16 in class (Snow 120) from 10:30 a.m. - 1:00 p.m.

  • EXAM III
    The Exam III is scheduled for Tuesday, November 17 in class
    Reminder: NO MAKE UP EXAMS

  • New Announcement:
    MATH 526 Tutoring on how to pull data into R and analyze it, with Alec Knutsen, math and computer science student at 4:00 p.m. on October 29, 2015 in Snow 120.
    Please bring your laptop if you have one!

  • The Exam II is a take home exam due Tuesday, November 3
    A sample of data for statistical analysis for the project as the Exam II.
    Additionally, the books by Richard De Veaux have many sets of data: Dr. De Veaux Data Sets.
    Another set of data: the Boston and NY marathons keep public records of past winners on their sites. For example: Martahon Data Sets

  • New Announcement from: Professor Pasik -Duncan


    Those students who believe that they can demonstrate confidently their knowledge required for the EXAM I but they didn't perform well on the Exam I on Tuesday, October 1 because the fire alarm went on 20 minutes before the end of the exam are invited to take the NEW EXAM I as the replacement of the original EXAM I on: Tuesday, October 20 during the class extended office hours: 9:00 am - 10:30 am in 503 Snow Hall. This is the only option.

    This exam won't have any curve, no extra credit, and its score will replace the current score even if it will be lower than the existing one. Since there won't be the extra credit problem the exam will last 30 min. The score on this new exam will be the final score for the EXAM I. Students must notify me about their decision to take this new EXAM I by midnight on Monday, October 19, and must agree to all conditions listed above.


  • The Exam I interrupted by the fire alarm last Thursday will be completed on Tuesday, October 6 in class. ALL STUDENTS are expected to be in class on Tuesday, October 6. NO MAKE UP EXAM WILL BE ARRANGED.


  • The Exam I is scheduled for Thursday, October 1 in class at 11:00 am ( 45 min - 100 pts)
    REMINDER: THERE ARE NO MAKE-UP EXAMS.
    NO CALCULATORS OF ANY TYPE ARE ALLOWED ON THE EXAM
    PLEASE BRING AN ID AND A PENCIL TO THE EXAM
    The Exam I will focus on testing the following concepts:
      1. Conditional Probability and Independence; Section 2.6
        Illustrative Examples: 2.34, 2.35, 2.36, 2.37, 2.38.
      2. Discrete Probability Distributions; Section 3.2
        Illustrative Examples: 3.9, 3.10
      3. Continuous Probability Distributions; Section 3.3
        Illustrative Examples: 3.11, 3.12, 3.13
      4. Joint Probability Distributions; Section 3.4
        Illustrative Examples: 3.14, 3.15, 3.16, 3.17, 3.18, 3.19, 3.20, 3.21
      5. Mean of a Random Variable, Section 4.1
        Illustrative Examples: 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7
      6. Variance and Covariance of Random Variables
        Illustrative Examples: 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16
      7. Binomial Distribution; Section 5,2
        Illustrative Examples: 5.1, 5.2, 5.3, 5.4,
      8. Normal Distribution and its Applications; Sections 6.2, 6.3, 6.4, 6.5
        Illustrative Examples: 6.2, 6.3, 6.4, 6.8, 6.15, 6.16

Resources

Homework Grading Policies and Expectations

  1. Weekly assignments of 10 problems will be collected at the beginning of class each Thursday. No late HW will be accepted.
  2. The student's name and "Math 526, HW #..." need to be clearly stated on the front page of each submission.
  3. Each problem is worth up to 2 points (so each assignment is out of 20 points in total), with:
    • 0 points for no solution or totally wrong approach
    • 1 point for correct reasoning but the lack of details in justification or/and wrong calculation
    • 2 points for correct reasoning with detailed justification
    Remarks: The focus of this course is on good understanding of mathematical statistics concepts; therefore arithmetic mistakes in this course are negligible, but I require that they be clearly marked. Grading has to be done in such a way that a student will know clearly what was the reason for losing points. Different approaches to finding solutions are encouraged and promoted; therefore looking at posted online solutions while grading students' work is not recommended. I recommend looking at a student's full assignment and providing any general comments or recommendations such as "your presentation requires improvement or significant improvement" at the end of the assignment.
  4. I expect to receive a weekly report/feedback from the grader. In this report I expect to see:
    • the record of points, mean, median, the lowest and the largest value and the standard deviation
    • the list of problems that left students with their concerns; in other words, which problems I should revisit to address students' lack of understanding
  5. Graded assignments will be returned to students in class on the following Thursday.
  6. At the end of the semester I will expect to receive a cumulative distribution of points and percentages with the same distribution characteristics as for each individual assignment.
  7. Students are responsible for collecting their graded HW assignments and for keeping them in their course portfolio as important evidence of their contributions.

Homework Assignments
HW # Exercises Due Date
#1 Chapter 2: 14, 36, 40, 50, 58, 74, 76, 101, 105, 113

Read Chapter 2		 09/03/2015
#2 Chapter 3: 5, 7, 12, 13, 14, 31, 36, 38, 40, 47.

Read Chapter 3, Sections 1 and 2		 9/10/2015
#3 Chapter 4: 2, 10, 12, 20, 34, 40, 48, 50, 60, 70
Read Chapter 4 		9/17/2015
#4 5.4, 5.10, 5.33, 5.42, 5.65
6.1, 6.6, 6.8, 6.18, 6.24
 9/24/2015
HW # 5 ( students will have the opportunity to complete their work on this HW in class on Thursday, October 8) Chapter 6:6.40, 6.41, 6.44, 6.45
Reading Assignment: Beta & Lognormal Distributions: Sections 6.8 & 6.9 		10/08/2015
#6 Chapter 8
Sections: 8.1& 8.2: 8.2, 8.6, 8.12, 8.14, 8.15
Sections: 8.3 & 8.4: 8.20, 8.23, 8.25, 8.28, 8.30
Reading assignment: Sampling distribution of S^2, t-distribution, chi- squared and F-distributions.
 10/22/2015
#7 Chapter 8: 8.38, 8.41, 8.44, 8.46, 8.49, 8.51, 8.64, 8.67, 8.73. 10/27/2015
#8 Chapter 9: 2, 5, 6, 14, 36, 41, 56, 69, 71, 72 11/10/2015
#9 Chapter 10:10.20, 10.23, 10.26, 10.31, 10.33

Reading assignment: Sections 10.2 & 10.3

Students are supposed to demonstrate their knowledge in the following concepts:
The Probability of a Type I and II Errors
The Power of the t Test
The User of P-Values for Decision Making in Testing Hypotheses 		11/12/2015
#10 Chapter 10 10.55, 10.57, 10.67, 10.68, 10.71 11/17/2015
#11 Chapter 10 10.80, 10.81, 10.86, 10.87, 10.88 11/24/2015
#12 Chapter 11 11.2, 11.3, 11.5, 11.8, 11.9 12/3/2015

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Lectures
Lecture # Subject Date
#1
  • Overview of the course and discussion of requirements and expectations.

  • Announcement of first writing assignment: Short Bio, due Tuesday 8/27/15.
    • Prepare a well-written, typed document that includes your name, year in school, intended major, what/when/where your last math class was, and at least one thing you hope to learn in Math 526.
    • In addition, briefly describe things like your awards/accomplishments, interests/hobbies, and goals.
    • For reference, see Prof. Pasik-Duncan's short bio on her website or in the August 2014 IFAC newsletter. These are only examples; your short bio can be shorter.
 8/25/2015
#2
  • Chapter 2: Probability
    • Section 2.1: Sample Space.
    • Section 2.2: Events.
    • Section 2.4: Probability of an Event.
    • Section 2.5: Addition Rules.
 8/27/2015
#3
  • Review Sections 2.2, 2.4, and 2.5.
  • Section 2.3: Counting Sample Points.
  • Section 2.6: Conditional Probability, Independence.
  • Bayes' Theorem and Its Applications.
9/1/2015
#4
  • Review Chapter 2 and Introduction to Chapter 3: Random Variables.
  • Reading Assignment: Read Chapter 3
 9/3/2015
#5
  • Joint Probability Distributions, Section 3.4
9/8/2015
#6
  • Chapter 4: Mathematical Expectation
 9/10/2015
#7
  • Chapter 5: Binomial, Hypergeometric, Negative Binomial and Geometric Distributions;
    Sections: 5.1, 5.2, 5.3, 5.4
9/15/2015
#8
  • Chapter 5 ( Continuation): Poisson Process, Section 5.5, and revisiting all basic discrete probability.
  • Introduction to Chapter 6: Uniform Distribution; Section 6.1
  • Read Chapter 5
9/17/2015
#9
  • Chapter 6: Normal Distribution and its Applications; Sections: 6.2, 6.3 & 6.4
  • Normal Approximation to the Binomial; Section 6.5
9/22/2015
#10
  • Gamma & Exponential Distributions; Ch-Squared Distribution; Sections: 6.6 & 6.7
  • Read Chapter 6
 9/24/2015
#11
  • Review before the Exam I which is scheduled for Thursday, October 1 in class.
  • Exam I is comprehensive and will covered sections:
    • 2.1 through 2.7
    • 3.1 through 3.4
    • 4.1 through 4.3
    • 5.1 through 5.5
    • 6.1 through 6.7
9/29/2015
#12
  • EXAM I (20%) - 45 minutes - 5 show your work well presented problems.
10/1/2015
#13
  • Chapter 6: Gamma, Exponential & Chi-Squared Distributions, Sections: 6.6 & 6.7
 10/06/2015
#14
  • Beta & Lognormal Distributions: Sections 6.8 & 6.9
10/08/2015
#15
  • Fall Break - No class, no HW, Enjoy the Break!
10/13/2015
#16
  • Chapter 8: Fundamental Sampling Distributions and Data Descriptions
    • Sections 8.1- 8.4: Important Statistics and Central Limit Theorem
 10/15/2015
#17
  • Chapter 8: Fundamental Sampling Distributions and Data Descriptions
    • Sections 8.4 - 8.8: Revisit Central Limit Theorem, Revisit Chi-Squared Distribution, t-distribution and F-distribution
 10/20/2015
#18
  • Chapter 9: Confidence Intervals for mean
    		•  10/22/2015
    #19
    • Chapter 9: Confidence Intervals for proportion, variance and difference in means with two samples,
    • Take Home Exam II with due on Tuesday, November 3 needs to be picked up in person in the classroom during the class time.
    		 10/27/2015
    #20 10/29/2015
    #21
    • Chapter 9: Confidence intervals for the mean, the difference between the means, a proportion, the difference between proportions and the variance
    		11/3/2015
    #22
    • No class meeting, independent study:
    • Review the following sections: 9.1, 9.2, 9.3, 9.4, 9.5, 9.8 (variances unknown but equal), 9.10, 9.11, 9.12
    		11/5/2015
    #23
    • Workshop in class over Chapter 9.
    • Introduction to Chapter 10: Testing Hypotheses
    		11/10/2015
    #24 Chapter 10: Tests of Hypotheses

    Review Before the Exam III:
    • Tests Concerning a Single Mean - Section 10.4
    • Tests on Two Means - Section 10.5
    • Test on a Single Proportion - Section 10.8
    • Tests on Two Proportions - Section 10.9
    • Test Concerning Variance - Section 10.10
    		11/12/2015
    #25 EXAM III IN CLASS

    Exam III consisting of four problems will cover:

    Chapters 9 & 10 - Confidence Intervals & Testing Hypotheses for:
    • A single mean with known and unknown variance with a small and a large size of sample
    • The difference of two means with known and unknown variances with a small and a large size of samples
    • A single proportion
    • A single variance
    • and will test on the use of tables for Normal distribution, t-distribution, and Chi-Squared distribution

    Illustrative Examples from the textbook serve as the best sample of the exam III problems:

    Confidence Intervals:
    • 9.2 page 271
    • 9.3 page 273
    • 9.5 page 275
    • 9.6 page 276
    • 9.10 page 286
    • 9.11 page 288
    • 9.14 page 297
    • 9.18 page 304

    Testing Hypotheses:
    • 10.3 & 10.4 page 338
    • 10.5 page 340
    • 10.6 page 344
    • 10.9 & 10.10 page 362
    • 10.12 page 366

    Good understanding of:
    How Does the Use of P-Values Differ from Classic Hypothesis Testing? pages: 333-334     		11/17/2015
    #26 Review after the Exam III - Students' feedback from the Exam III (for extra credit of 5 pts)
    Goodness-of-Fit Test and Test for Independence - Sections 10.11 & 10.12     		11/19/2015
    #27 Test for Homogeneity - Section 10.13 11/24/2015
    # NO CLASS - THANKSGIVING HOLIDAY
    Happy Thanksgiving to you and your families! Enjoy the break!
    - Bozenna Pasik-Duncan     		11/26/2015
    #28 Chapter 11 - Simple Linear Regression
    Least Squares and the Fitted Model - Section 11.3
    A measure of quality of fit: Coefficient of determination

    Working in Groups on Problems of Goodness of Fit & Linear Regression     		12/1/2015
    #29 Properties of Least Squares Estimators - Section 11.4
    SELF-EVALUATION MUST BE TURNED IN     		12/3/2015
    #30 Introduction to Analysis of Variance 12/8/2015
    #31 Closing Discussion on the Importance of Statistics in Every Day Life. Celebrating the end of the semester. 12/10/2015