APPA 5001: Probability Foundations for Data Science and AI 1
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- Course Type: Pathway | Breadth
- Specialization: Foundations of Probability and Statistics
- Instructor: Dr. Anne Dougherty, Senior Instructor, University of Colorado Teaching Professor in Applied Mathematics, Associate Department Chair, Undergraduate Studies Chair
- Prior knowledge needed:
- Programming languages: Intro to R programming
- Math: Calculus 1 and 2
- Technical requirements:
Learning Outcomes
- Explain why probability is important to statistics and data science.
- See the relationship between conditional and independent events in a statistical experiment.
- Calculate the expectation and variance of several random variables and develop some intuition. as to what powers the Internet.
- Develop a client and server with socket programming.
Course Grading Policy
| Assignment | Percentage of Grade |
|---|---|
| Week 1 | |
| Homework: Axioms of Probability | 8% |
| Homework: Descriptive Statistics and the Axioms of Probability | 5% |
| Week 2 | |
| Homework: Bayes Theorem | 8% |
| Homework: Conditional Probability | 5% |
| Week 3 | |
| Homework: Calculations with Discrete Random Variables | 8% |
| Homework: Discrete Random Variables | 5% |
| Week 4 | |
| Homework: Continuous Random Variables and Normal Random Variables | 8% |
| Homework: Continuous Random Variables | 5% |
| Week 5 | |
| Homework: Calculations of Covariance and Correlation in Various Examples | 8% |
| Homework: Joint Distributions and Covariance | 5% |
| Week 6 | |
| Homework: Working with Normal Random Variables and the CLT | 8% |
| Homework: Homework: Central Limit Theorem | 5% |
| Week 7 | |
| Final Exam | 22% |
Course Content
Duration: 9 hours
Understand the foundations of probability and its relationship to statistics and data science. We’ll learn what it means to calculate a probability, independent and dependent outcomes, and conditional events. We’ll study discrete and continuous random variables and see how this fits with data collection. We’ll end the course with Gaussian (normal) random variables and the Central Limit Theorem and understand it’s fundamental importance for all of statistics and data science.
Duration: 7 hours
**Could be changed** The notion of “conditional probability” is a very useful concept from Probability Theory and in this module we introduce the idea of “conditioning” and Bayes’ Formula. The fundamental concept of “independent event” then naturally arises from the notion of conditioning. Conditional and independent events are fundamental concepts in understanding statistical result
Duration: 8 hours
The concept of a “random variable” (r.v.) is fundamental and often used in statistics. In this module we’ll study various named discrete random variables. We’ll learn some of their properties and why they are important. We’ll also calculate the expectation and variance for these random variables.ap file containing a single TCP flow to determine the maximum bytes in flight—a hands-on exploration of the week's concepts.
Duration: 9 hours
In this module, we’ll extend our definition of random variables to include continuous random variables. The concepts in this unit are crucial since a substantial portion of statistics deals with the analysis of continuous random variables. We’ll begin with uniform and exponential random variables and then study Gaussian, or normal, random variables.
Duration: 8 hours
The power of statistics lies in being able to study the outcomes and effects of multiple random variables (i.e. sometimes referred to as “data”). Thus, in this module, we’ll learn about the concept of “joint distribution” which allows us to generalize probability theory to the multivariate case.
Duration: 7 hours
The Central Limit Theorem (CLT) is a crucial result used in the analysis of data. In this module, we’ll introduce the CLT and it’s applications such as characterizing the distribution of the mean of a large data set. This will set the stage for the next course.
Duration: 1 hour
Final Exam Format: Proctored Exam
You will complete a proctored exam worth 22% of your grade made up of made up of multiple choice and free response questions. You must attempt the final in order to earn a grade in the course. If you've upgraded to the for-credit version of this course, please make sure you review the additional for-credit materials in the Introductory module and anywhere else they may be found.
Notes
- Cross-listed Courses: Courses that are offered under two or more programs. Considered equivalent when evaluating progress toward degree requirements. You may not earn credit for more than one version of a cross-listed course.
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