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This course is part of Data Science Foundations: Statistical Inference Specialization
Instructors: Anne Dougherty
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(245 reviews)
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Intermediate level
Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.
(245 reviews)
Recommended experience
Intermediate level
Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.
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.
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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 its fundamental importance for all of statistics and data science.
This course can be taken for academic credit as part of CU Boulder’s Master of Science in Data Science (MS-DS) degree offered on the Coursera platform. The MS-DS is an interdisciplinary degree that brings together faculty from CU Boulder’s departments of Applied Mathematics, Computer Science, Information Science, and others. With performance-based admissions and no application process, the MS-DS is ideal for individuals with a broad range of undergraduate education and/or professional experience in computer science, information science, mathematics, and statistics. Learn more about the MS-DS program at https://www.coursera.org/degrees/master-of-science-data-science-boulder Logo adapted from photo by Christopher Burns on Unsplash.
Welcome to the course! This module contains logistical information to get you started!
3 readings1 discussion prompt1 ungraded lab
Understand the foundation 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.
3 videos2 readings1 assignment1 programming assignment1 ungraded lab
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 results.
2 videos1 reading1 assignment1 programming assignment1 ungraded lab
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.
4 videos1 reading1 assignment1 programming assignment1 ungraded lab
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.
4 videos2 readings1 assignment1 programming assignment1 ungraded lab
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.
3 videos1 reading1 assignment1 programming assignment
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.
2 videos1 reading1 assignment1 programming assignment1 ungraded lab
We asked all learners to give feedback on our instructors based on the quality of their teaching style.
CU Boulder is a dynamic community of scholars and learners on one of the most spectacular college campuses in the country. As one of 34 U.S. public institutions in the prestigious Association of American Universities (AAU), we have a proud tradition of academic excellence, with five Nobel laureates and more than 50 members of prestigious academic academies.
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This course is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹
This course is part of the following degree program(s) offered by University of Colorado Boulder. If you are admitted and enroll, your completed coursework may count toward your degree learning and your progress can transfer with you.¹
University of Colorado Boulder
Degree · 2 years
¹Successful application and enrollment are required. Eligibility requirements apply. Each institution determines the number of credits recognized by completing this content that may count towards degree requirements, considering any existing credits you may have. Click on a specific course for more information.
245 reviews
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3.67%
1.63%
6.53%
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Reviewed on Jun 2, 2024
Thank you to everyone who put a lot of effort into making this course; it is really helpful.
Reviewed on Oct 10, 2021
The instructor is very good, more examples need to be added, there are mistakes in the evaluation
Reviewed on Mar 4, 2023
This course taught me the basics of probability, R programming, and Latex. I am deeply grateful to Prof. Anne Dougherty, UC Boulder, and Coursera for this tough but wonderful experience.
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