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 is part of the Statistical Inference for Data Science Applications Specialization

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## About this Course

Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.

### What you will learn

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.

## Skills you will gain

Sequence in calculus up through Calculus II (preferably multivariate calculus) and some programming experience in R.

## Offered by

### University of Colorado Boulder

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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## Syllabus - What you will learn from this course

**9 hours to complete**

## Descriptive Statistics and the Axioms of Probability

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.

**9 hours to complete**

**7 hours to complete**

## Conditional Probability

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.

**7 hours to complete**

**8 hours to complete**

## Discrete Random Variables

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.

**8 hours to complete**

**9 hours to complete**

## Continuous Random Variables

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.

**9 hours to complete**

## About the Statistical Inference for Data Science Applications Specialization

This program is designed to provide the learner with a solid foundation in probability theory to prepare for the broader study of statistics. It will also introduce the learner to the fundamentals of statistics and statistical theory and will equip the learner with the skills required to perform fundamental statistical analysis of a data set in the R programming language.

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