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.

# Probability Theory: Foundation for Data Science

This course is part of Data Science Foundations: Statistical Inference Specialization

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## What you'll 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'll gain

## Details to know

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6 quizzes

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## There are 7 modules in this course

Welcome to the course! This module contains logistical information to get you started!

#### What's included

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.

#### What's included

3 videos2 readings1 quiz1 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.

#### What's included

2 videos1 reading1 quiz1 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.

#### What's included

4 videos1 reading1 quiz1 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.

#### What's included

4 videos2 readings1 quiz1 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.

#### What's included

3 videos1 reading1 quiz1 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.

#### What's included

2 videos1 reading1 quiz1 programming assignment1 ungraded lab

### Instructors

### Offered by

### Recommended if you're interested in Probability and Statistics

University of Colorado Boulder

University of Colorado Boulder

University of Colorado Boulder

University of Colorado Boulder

## Build toward a degree

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

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