Math 627: Probability

MATH 627: This course focuses on: 1. Probability Distributions of Random Variables of Discrete and Continuous Type 2. Bivariate Distributions 3. Probability Distributions of Functions of One and Two Random Variables 4. Limit Theorems of Probability

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



Announcements

  • New Announcement Final Exam
    The Final Exam is scheduled for Thursday, December 17 in class (Snow 454) from 1:30-4:00 p.m.

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

  • The Exam II is a take home exam due Tuesday, November 3

  • The Exam I is scheduled for Thursday, October 1 in class at 2:30 pm ( 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 Independent Events ; Section 1.3 & 1.4
        Illustrative Examples: 1.3-2, 3, 4, 5, 6, 7 ; 1.4-1, 2, 3, 4, 5
      2. Discrete Probability Distributions; Section 2.1; 2.2; 2.3; 2.4
        Illustrative Examples: 2.1-3, 4, 5, 6, 2.2-1, 2, 3, 4, 2.3-1, 2, 5, 7, 2.4-1, 2, 3, 4, 5, 7, 89, 10,
      3. Continuous Probability Distributions; Section 3.1 & 3.3
        Illustrative Examples: 3.1-1, 2, 3, 3.2-1, 2, 3, 4, 5, 6, 7
      4. Joint Probability Distributions; Section 4.1 & 4.2
        Illustrative Examples: 4.1-1, 2, 3, 4, 4.2- 1, 3
  • 9/4/2015:
    From Professor Pasik-Duncan,

    MATH 627 has been moved to 330 Strong. There are 4 people who are on the waiting list. But the waiting list doesn’t work any more and it is past the deadline to add a course through Enroll & Pay, so those students have to use a schedule change form to enroll. They have until Sept 14 to enroll with the Schedule Change Form, which is available at this link.The form requires an “instructor signature”. I will sign it. Only students who have been attending class will get my permission.

Resources

Homework Grading Policies and Expectations

  1. Weekly assignments of will be collected at the beginning of class each Thursday. No late HW will be accepted.
  2. The student's name and "Math 627, HW #..." need to be clearly stated on the front page of each submission.
  3. Each problem is worth up to 2 points, 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.

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Homework Assignments
HW # Exercises Due Date
#1 Chapter 1: Choose 2 problems from each of 5 sections 9/3/2015
#2 Section 2.1: 3
Section 2.2: 1,2,4,8		 9/10/2015
#3 Section 2.3: 2,8,11,16
Section 2.4: 6, 8, 9, 11, 19, 20
Read Chapter 2		 9/17/2015
#4 2.5 - 5; 2.5 - 6; 2.6 - 2, 2.6 - 4, 2.6 - 10
3.1 - 4, 3.1 - 8, 3.1 - 20, 3.2 - 8, 3.3 - 6 		9/24/2015
# 5 ( students will work on it in class on Thursday) Chapter 4: 4.1-3, 4.2-7, 4.3-2, 4.4-1, 4.4-17 10/08/2015
#6 Chapter 5 - 5.1-2, 5.1-6, 5.1- 8, 5.1-9, 5.1-10, 5.1-12, 5.1-13, 5.1- 14, 5.1- 15, 5.2-1

Reading Assignment: Transformations of Two Random Variables, Section 5.2

10/22/2015
#7 Chapter 5 - 5.4-2, 5.4-3, 5.4- 4, 5.4-5, 5.4-7, 5.4-9, 5.4-10, 5.4- 21, 5.5- 1, 5.5-13


10/27/2015
#8
  • Chapter 5: 5.6-4, 5.6-6, 5.6-8, 5.7- 9, 5.7-11, 5.7-12, 5.8-2, 5.8-5, 5.9-3, 5.9-5.
  • Reading Assignment: Central Limit Theorem, Approximations for Discrete Distributions, Chebyshev's Inequality, Limiting Moment Generating Functions
 11/10/2015
#9 Section 6.4: 1, 2, 3, 5, 6
11/12/2015
#10 Chapter 6.4: 6.4-7(a),(b), 6.4-8, 6.4-9, 6.4-11, 6.4-12 11/17/2015
#11 Chapter 6.3: 6.3-1, 6.3-3, 6.3-6, 6.3-10, 6.3-11 ((d) is optional) 11/24/2015
#12 Chapter 6.6: 6.6-1, 6.6-2, 6.6-3, 6.6-4 on page 280 12/3/2015

Lectures
Lecture # Subject Date
#1
  • Overview of the course
 8/25/2015
#2
  • Chapter 1: Introduction to Probability
  • Counting Probabilities
  • Independent Events
8/27/2015
#3
  • Chapter 1: Condition Probability and Bayes' Theorem
 9/1/2015
#4
  • Chapter 2 & 3: Random Variables of Discrete & Continuous Types
  • Probability Distribution Function
  • Probability Mass Function and Probability Density Function
  • Expectation and Variance of Random Variable
9/3/2015
#5
  • Special Mathematical Expectations; Moment Generating Function, Section 2.3
 9/7/2015
#6
  • Binomial Distribution, Section 2.4
 9/10/2015
#7
  • Chapter 2: Binomial, Hypergeometric, Negative Binomial, Geometric, Poisson Distributions;
    Sections: 2.4 through 2.6
9/17/2015
#8
  • Chapter 2- Review all basic discrete probability.

  • Introduction to Chapter 3: Uniform Distribution; Moment Generating Function; Section 3.1

  • Read Section 3.2: The Exponential, Gamma and Chi- Square Distributions
9/17/2015
#9
  • The Exponential, Gamma and Chi- Square Distributions; Section 3.2
9/22/2015
#10
  • Chapter 3: Normal Distribution and its Applications; Normal Approximation to the Binomial;
    Section 3.3
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:
    • 1.1 through 1.5
    • 2.1 through 2.6
    • 3.1 through 3.3
    • Sections 4.1,4.2
 9/29/2015
#12
  • EXAM I (20%) - 45 minutes - 5 show your work problems with a focus on well presented solutions.
10/1/2015
#13
  • Chapter 4:
      Bivariate Distributions of Discrete and Continuous Types
      The Correlation Coefficient
      Conditional Distribution
  • Comment on the last question in class:
      That conditional probability that X takes on a single value is 0! Big thanks to the student for his kind comment. I will return to this comment in class. Thank you!
10/6/2015
#14
  • Practice Problems
  • Review Chapter 4
 10/8/2015
#15
  • Fall Break - No class, no HW, Enjoy the Break!
10/13/2015
#16
  • Chapter 5 : Distributions of Functions of Random Variables
    • Section 5.1: Functions of One Random Variable
10/15/2015
#17
  • Chapter 5 : Distributions of Functions of Random Variables
    • Sections 5.2 & 5.4: Transformations of Two Random Variables and Revisiting the Moment Generating Function Technique
 10/20/2015
#18
  • Chapter 5: Moment generating function, unbiased estimators
 10/22/2015
#19
  • Chapter 5: Convergence in distribution and in probability
  • 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 5: Central Limit Theorem, Approximations for Discrete Distributions, Chebyshev's Inequality, Limiting Moment Generating Functions
 11/3/2015
#22
  • No class meeting, independent study: Review the following sections: 5.6, 5.7, 5.8, 5.9
11/5/2015
#23
  • Workshop in class over sections: 5.6-5.9 .
  • Proof of the Central Limit Theorem, Convergence in Probability
11/10/2015
#24 Review Before the Exam III:
  • Functions of One Random Variable, Section 5.1
  • Transformations of Two Random Variables, Section 5.2
  • The Moment Generating Function Technique, Section 5.4
  • The Central Limit Theorem & Approximations for Discrete Distributions, Sections 5.6 & 5.7
  • Maximum Likelihood Estimator & Unbiased Estimators, Section 6.4
 11/12/2015
#25 EXAM III IN CLASS

Exam III consisting of four or five problems will cover:

Selected Sections from Chapters 5 & 6 - Distributions of Functions of Random Variables & Point Estimation
  • Functions of One Random Variable, Section 5.1
  • Transformations of Two Random Variables, Section 5.2
  • The Moment Generating Function Technique, Section 5.4
  • The Central Limit Theorem & Approximations for Discrete Distributions, Sections 5.6 & 5.7
  • Maximum Likelihood Estimator & Unbiased Estimators, Section 6.4

20 Illustrative Examples from the textbook serve as the best sample of the exam III problems:
  • 5.1-3 page 166
  • 5.1-5 page 169
  • 5.2-1 page 172
  • 5.2-2 page 173
  • 5.2-3 page 175
  • 5.4-2 & 5.4-3 page 189
  • 5.6-1, 5.6-2, & 5.6-3 page 201
  • 5.7-2, 5.7-3, 5.7-4, & 5.7-5 pages 208-209
  • 6.4-1, 6.4-2, 6.4-3, 6.4-4, & 6.4-5 pages 259-262

Remark: Reviewing homework is strongly recommended! 		11/17/2015
#26 Review after the Exam III - Students' feedback from the Exam III (for extra credit of 5 pts)
Order Statistics, Section 6.3 		11/19/2015
#27 The applications of Order Statistics 11/24/2015
# NO CLASS - THANKSGIVING HOLIDAY
Happy Thanksgiving to you and your families! Enjoy the break!
- Bozenna Pasik-Duncan 		11/26/2015
#28 Maximum Likelihood Estimator and Its Asymptotic Distribution, Section 6.6

Working in Groups on Problems 		12/1/2015
#29 Maximum Likelihood Estimator and Its Asymptotic Distribution, Section 6.6 (Continuation)
SELF-EVALUATION MUST BE TURNED IN 		12/3/2015
#30 Probability and Statistics in modeling data. 12/8/2015
#31 Closing Discussion on the Importance of Probability & Statistics in Every Day Life. Celebrating the end of the semester. 12/10/2015