Exploration of Data Science requires certain background in probability and statistics. This course introduces you to the necessary sections of probability theory and statistics, guiding you from the very basics all way up to the level required for jump starting your ascent in Data Science.

This course is part of the Mathematics for Data Science Specialization

# Probability Theory, Statistics and Exploratory Data Analysis

Offered By

## About this Course

#### 100% online

#### Course 4 of 4 in the

#### Flexible deadlines

#### Approx. 23 hours to complete

#### English

## Syllabus - What you will learn from this course

**3 hours to complete**

## Conditional probability and Independence

During this week we discuss conditional probability and independence of events. Sometimes we can use this definition to find probabilities. Sometimes we check that this definition fulfills to assure whether events are independent. We discuss important law of total probability, which allows us to find probability of some event when we know its conditional probabilities provided some hypotheses and probabilities of the hypotheses. We also discuss Bayes's rule which allows us to find probability of hypothesis provided that some event occurred. We demonstrate how Python can be used for calculating conditional probabilities and checking independence of events.

**3 hours to complete**

**13 videos**

**7 practice exercises**

**3 hours to complete**

## Random variables

Random variable denotes a value that depends on the result of some random experiment. Some natural examples of random variables come from gambling and lotteries. There are two main classes of random variables that we will consider in this course. This week we'll learn discrete random variables that take finite or countable number of values. Discrete random variables can be described by their distribution. We'll consider various discrete distributions, introduce notions of expected value and variance and learn to generate and visualize discrete random variables with Python.

**3 hours to complete**

**15 videos**

**3 practice exercises**

**3 hours to complete**

## Systems of random variables; properties of expectation and variance, covariance and correlation.

Several random variables associated with the same random experiment constitute a system of random variables. To describe system of discrete random variables one can use joint distribution, which takes into account all possible combinations of values that random variables may take. We'll find some joint distributions, research their properties and introduce independence of random variables. Then we'll discuss properties of expected value and variance with respect to arithmetic operations and introduce measures of independence between random variables.

**3 hours to complete**

**16 videos**

**7 practice exercises**

**3 hours to complete**

## Continuous random variables

This week we'll study continuous random variables that constitute important data type in statistics and data analysis. For continuous random variables we'll define probability density function (PDF) and cumulative distribution function (CDF), see how they are linked and how sampling from random variable may be used to approximate its PDF. We'll introduce expected value, variance, covariance and correlation for continuous random variables and discuss their properties. Finally, we'll use Python to generate independent and correlated continuous random variables.

**3 hours to complete**

**16 videos**

**8 practice exercises**

### Reviews

#### 3.9

##### TOP REVIEWS FROM PROBABILITY THEORY, STATISTICS AND EXPLORATORY DATA ANALYSIS

A nice introduction for beginners and those who need a warm up.

## Start working towards your Master's degree

### About National Research University Higher School of Economics

## About the Mathematics for Data Science Specialization

## Frequently Asked Questions

When will I have access to the lectures and assignments?

Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

What will I get if I subscribe to this Specialization?

When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

What is the refund policy?

Is financial aid available?

More questions? Visit the Learner Help Center.