Probability

In this course we shall:

• review counting techniques

• construct probability theory axiomatically

• apply techniques from probability theory to solve real-world problems

• utilize electronic tools in dealing with probability

• establish theoretical foundations to statistical methods

This course shall cover nine chapters namely:

0. Counting

1. Probability

2. Random Variables, Distribution Functions, and Expectations

3. Some Special Distributions

4. Functions of Random Variables

5. Joint and Marginal Distributions

6. Conditional Distribution and Stochastic Independence

7. Sampling and Sampling Distributions

8. Law of Large Numbers and Central Limit Theorem

Calculus 3 is a prerequisite to the course. Integrals will be applied to most calculations starting from Chapter 2. Familiarity with basic statistics is also useful. The end-goal of this course is to establish theoretical foundations to statistics including distributions and expectation.

Technology will be used extensively for the whole semester. Hence, the availability of electronic devices (such as smartphones or laptops) and internet connectivity will be advantageous.

• 32 Lecture Exercises (one from each lecture)

• 9 Quizzes (one from each chapter)

• 2 Major Examinations (one from each term period)

• 1 Project

Cut-off score is 50% for all course requirements.

Answers to lecture exercises and quizzes shall be written in sheets of 1/4 of short-sized bond paper. Take a photo of each page and send them as attachment to my e-mail address jdselle@up.edu.ph with subject properly indicating which course requirement is being submitted (for example "Math-C 229 Quiz No. 1"). Then, in the body of the mail, write your full name, course, year, and block section (I encourage you to do this in formal and complete sentences). The reason why it is required to write in 1/4 sheets is to enhance visibility. (Photos of whole-sized paper are sometimes difficult to read). You are allowed to use as many 1/4 sheets as you would need.

Subject to circumstances, major exams will be conducted in the campus. This shall be properly arranged and instructions shall be announced to you.

• Ross (2014). A first course in probability. Pearson

• Mood, Graybill, & Boes (1963). Introduction to the theory of statistics. McGraw-Hill, Inc.

• Hogg, Craigg, McKean (2019). Introduction to mathematical statistics, 8th Ed.