## Course Syllabus for "MA252: Introduction to Probability Theory"

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This course will introduce you to the fundamentals of probability theory and random processes. The theory of probability was originally developed in the 17th century by two great French mathematicians, Blaise Pascal and Pierre de Fermat, to understand gambling. Today, the theory of probability has found many applications in science and engineering. Engineers use data from manufacturing processes to sample characteristics of product quality in order to improve the products being produced. Pharmaceutical companies perform experiments to determine the effect of a drug on humans and use the results to make decisions about treatment of illnesses, while economists observe the state of the economy over periods of time and use the information to forecast the economic future. In this course, you will learn the basic terminology and concepts of probability theory, including random experiments, sample spaces, discrete distribution, probability density function, expected values, and conditional probability. You will also learn about the fundamental properties of several special distributions, including binomial, geometric, normal, exponential, and Poisson distributions, as well as how to use them to model real-life situations and solve applied problems.

### Learning Outcomes

Upon successful completion of this course, you will be able to:

- define probability,sample space, events, and probability functions;
- use combinations to evaluate the probability of outcomes in coin-flipping experiments;
- calculate the probability of union and intersection of events and conditional probability;
- apply Bayes’ theorem to simple situations;
- calculate the expected values of discrete and continuous random variables;
- determine the distribution of the sums of random variables;
- calculate cumulative distributions and marginal distributions;
- use random processes to model and predict phenomena governed by binomial, multinomial, geometric, exponential, normal, and Poisson distributions; and
- explain and use the law of large numbers and the central limit theorem.

### Course Requirements

In order to take this course, you must:

√ have access to a computer;

√ have continuous broadband Internet access;

√ have the ability/permission to install plug-ins or software (e.g., Adobe Reader or Flash);

√ have the ability to download and save files and documents to a computer;

√ have the ability to open Microsoft files and documents (.doc, .ppt, .xls, etc.);

√ have competency in the English language;

√ have read the Saylor Student Handbook; and

√ have completed MA101, MA102, MA103, MA211, and MA221, or their equivalents.

### Course Information

**Welcome to MA252: **Introduction to Probability Theory. General
information on this course and its requirements can be found below.

**Primary Resources:** This course is comprised of a range of different
free online materials. However, the course makes primary use of the
following materials:

- Massachusetts Institute of Technology OpenCourseWare: Professor Dmitry Panchenko’s Math 18.05: Introduction to Probability and Statistics Lecture Notes (HTML)
- YouTube: UCLA: Professor Herbert Enderton’s Math 3C: Math and Probability for Life Sciences Lecture Series (YouTube)
- Khan Academy: Salman Khan’s Probability Lecture Series (YouTube)
- Dartmouth College: Professors Charles M. Grinstead and J. Laurie Snell’s Introduction to Probability (PDF)

**Requirements for Completion:** In order to complete this course, you
will need to work through each unit and all of its assigned materials,
including the readings, lectures, and practice assignments. Pay special
attention to Unit 1 and Unit 2, as these lay the groundwork for
understanding the more advanced material presented in the later units.

In order to pass this course, you will need to complete the final exam
and earn 70% or higher. Your score on the exam will be tabulated as soon
as you finish it. If you do not pass the exam, you may take it again.

Note that you will only receive an official grade on your final exam.
However, in order to adequately prepare for it, you will need to work
through all the readings, lectures, and practice assignments in the
course.

**Time Commitment:** This course should take you a total of **115.25**
hours. Each unit includes a time advisory that lists the amount of time
you are expected to spend on each subunit. These advisories should help
you plan your time accordingly. It may be useful to take a look at the
time advisories, determine how much time you have over the next few
weeks to complete each unit, and then set goals for yourself. For
example, Unit 1 should take you approximately 18.75 hours. Perhaps you
can sit down with your calendar and decide to complete Subunit 1.1 (a
total of 7 hours) on Monday and Tuesday nights, Subunit 1.2 (a total of
10.5 hours) on Wednesday and Thursday nights, etc.

**Table of Contents:** You can find the course's units at the links below.