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Probability Theory: Foundation for Data Science
  • Level Professional
  • المدة 48 ساعات hours
  • الطبع بواسطة University of Colorado Boulder
  • Offered by

عن

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.

الوحدات

Welcome to Probability Theory

    • 3 Readings
    • 1 Discussion
    • 1 Lab
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1 Discussions

  • Introduce Yourself

1 Labs

  • Introduction to Jupyter Notebooks and R

3 Readings

  • Earn Academic Credit for your Work!
  • Course Support
  • Course Resources and Reading

Introduction to Probability

    • 1 Videos
    • 1 Readings
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1 Videos

  • Intro to Probability

1 Readings

  • Intro to Probability

Remaining Lectures

    • 2 Videos
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2 Videos

  • Axioms of Probability
  • Counting: Permutations and Combinations

Assessments

    • 1 Readings
    • 1 Quiz
    • 1 Lab
    • 1 Programming
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1 Programming

  • Homework: Axioms of Probability

1 Labs

  • Guided Exploratory Ungraded Lab

1 Readings

  • Introducing the formula sheet for this course

1 Quiz

  • Homework: Descriptive Statistics and the Axioms of Probability

Conditional Probability and Bayes Theorem

    • 1 Videos
    • 1 Readings
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1 Videos

  • Conditional Probability and Bayes Theorem

1 Readings

  • Conditional Probability and Bayes Theorem

Independent Events

    • 1 Videos
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1 Videos

  • Independent Events

Assessments

    • 1 Quiz
    • 1 Lab
    • 1 Programming
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1 Programming

  • Homework: Bayes Theorem

1 Labs

  • Guided Exploratory Ungraded Lab

1 Quiz

  • Homework: Conditional Probability

Introduction to Discrete Random Variables

    • 1 Videos
    • 1 Readings
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1 Videos

  • Discrete Random Variables

1 Readings

  • Discrete Random Variables

Examples of Discrete Random Variables

    • 3 Videos
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3 Videos

  • Bernoulli and Geometric Random Variables
  • Expectation and Variance
  • Binomial and Negative Binomial Random Variables

Assessments

    • 1 Quiz
    • 1 Lab
    • 1 Programming
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1 Programming

  • Homework:  Calculations with Discrete Random Variables

1 Labs

  • Guided Exploratory Ungraded Lab

1 Quiz

  • Homework: Discrete Random Variables

Introduction to Continuous Random Variables

    • 1 Videos
    • 1 Readings
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1 Videos

  • Continuous Random Variables

1 Readings

  • Continuous random variables

Normal (Gaussian) Random Variable

    • 2 Videos
    • 1 Readings
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2 Videos

  • The Gaussian (normal) Random Variable Part 1
  • The Normal Random Variable Part 2

1 Readings

  • Normal Random Variable

Additional Continuous Random Variables

    • 1 Videos
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1 Videos

  • The Poisson and Exponential Random Variables

Assessments

    • 1 Quiz
    • 1 Lab
    • 1 Programming
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1 Programming

  • Homework: Continuous Random Variables and Normal Random Variables

1 Labs

  • Guided Exploratory Ungraded Lab

1 Quiz

  • Homework: Continuous Random Variables

Introduction to Covariance and Correlation

    • 1 Videos
    • 1 Readings
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1 Videos

  • Covariance and Correlation

1 Readings

  • Covariance and Correlation

Additional topics in Expectation and Variance

    • 2 Videos
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2 Videos

  • More on Expectation and Variance
  • Jointly Distributed Random Variables

Assessments

    • 1 Quiz
    • 1 Programming
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1 Programming

  • Homework: Calculations of Covariance and Correlation in Various Examples

1 Quiz

  • Homework: Joint Distributions and Covariance

The Central Limit Theorem

    • 2 Videos
    • 1 Readings
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2 Videos

  • Introduction to the Central Limit Theorem
  • Central Limit Theorem Examples

1 Readings

  • Central Limit Theorem

Assessments

    • 1 Quiz
    • 1 Lab
    • 1 Programming
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1 Programming

  • Homework: Working with Normal Random Variables and the CLT

1 Labs

  • Guided Exploratory Ungraded Lab

1 Quiz

  • Homework: Central Limit Theorem

Auto Summary

Discover the foundations of probability and its critical role in data science with this engaging course led by Coursera. Dive into calculating probabilities, understanding independent and dependent outcomes, and exploring conditional events. Study discrete and continuous random variables, Gaussian distributions, and the Central Limit Theorem. Perfect for professionals in maths, statistics, and data science, this course is part of CU Boulder’s MS-DS degree. Available through Starter and Professional subscriptions, it offers 2880 minutes of in-depth content for a comprehensive learning experience.

Anne Dougherty
Instructors

Anne Dougherty

Jem Corcoran
Instructors

Jem Corcoran