STAT 414: Introduction to Probability Theory

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course overview

STAT 414 focuses on the theory of introductory probability. The course goals are:

  1. To learn the theorems of basic probability.
  2. To learn applications and methods of basic probability.
  3. To develop theoretical problem-solving skills.

course topics

Probability spaces, discrete and continuous random variables, transformations, expectations, generating functions, conditional distributions, law of large numbers, central limit theorems.

Here is a link to the Online Notes for STAT 414.


The official prerequisites are a standard three course calculus sequence (for example, MATH 140, MATH 141 and MATH 230) and knowledge of Matrix Algebra (see Review) / Linear Algebra (MATH 220). If it has been some time since you’ve studied calculus, you might want to get yourself a good reference and do some quick reviewing. The calculus techniques most frequently used in the course include: differentiation, integration, series, and limits, (See Review).  You may be expect to be tested on these foundational concepts and skills at the beginning of the course.  Also, MAS students are also strongly encouraged to complete application courses STAT 500 and STAT 501 before taking STAT 414.


Hogg, R.V., and Tanis, E.A. (2015). Probability and Statistical Inference, Prentice Hall, 9th edition. (We will primarily cover chapters 1-5.)


Students must have immediate access to a printer/scanner in order to scan hand written assignments into .pdf documents and upload them into Canvas.

assessment plan

Quizzes - 10
Exams - 5

PLEASE NOTE: This course may require you to take exams using certain proctoring software that uses your computer’s webcam or other technology to monitor and/or record your activity during exams. The proctoring software may be listening to you, monitoring your computer screen, viewing you and your surroundings, recording and storing any and all activity (including visual and audio recordings) during the proctoring process. By enrolling in this course, you consent to the use of the proctoring software selected by your instructor, including but not limited to any audio and/or visual monitoring which may be recorded. Please contact your instructor with any questions(Read more...)

academic integrity

All Penn State policies regarding ethics and honorable behavior apply to this course. Academic integrity is the pursuit of scholarly activity free from fraud and deception and is an educational objective of this institution. All University policies regarding academic integrity apply to this course. Academic dishonesty includes, but is not limited to, cheating, plagiarizing, fabricating of information or citations, facilitating acts of academic dishonesty by others, having unauthorized possession of examinations, submitting work of another person or work previously used without informing the instructor, or tampering with the academic work of other students.

For any material or ideas obtained from other sources, such as the text or things you see on the web, in the library, etc., a source reference must be given. Direct quotes from any source must be identified as such.

All exam answers must be your own, and you must not provide any assistance to other students during exams. Any instances of academic dishonesty WILL be pursued under the University and Eberly College of Science regulations concerning academic integrity. For more information on academic integrity, see Penn State's statement on plagiarism and academic dishonesty.

The Eberly College of Science Code of Mutual Respect and Cooperation embodies the values that we hope our faculty, staff, and students possess and will endorse to make The Eberly College of Science a place where every individual feels respected and valued, as well as challenged and rewarded.


Penn State welcomes students with disabilities into the University's educational programs. If you have a disability-related need for reasonable academic adjustments in this course, contact the Office for Disability Services (ODS) at 814-863-1807 (V/TTY). For further information regarding ODS, please visit the Office for Disability Services Web site at

In order to receive consideration for course accommodations, you must contact ODS and provide documentation (see the documentation guidelines at If the documentation supports the need for academic adjustments, ODS will provide a letter identifying appropriate academic adjustments. Please share this letter and discuss the adjustments with your instructor as early in the course as possible. You must contact ODS and request academic adjustment letters at the beginning of each semester.

course author

Dr. Laura Simon is the primary author of the materials for this course and has taught this course in residence several semesters.

Other Course Content Contributors include: Dr. Murali Haran, Dr. Damla Senturk and Dr. Tracey Hammel.