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.

Offered By

## About this Course

### Offered by

#### National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more.

## Start working towards your Master's degree

## 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**

**1 reading**

**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

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

Very nice approach to such a vast topic , making it more understandable. Such type of interactive lectures are advisable for courses on Calculus and Algebra from the same University.

Ilya Schurov explains concepts very well, and this course is a great start to begin the journey into data science. Also, the inclusion of some programming is appreciated!

Excellent course. To the point with no fluff. The professor explained everything in just the right amount of detail and the inclusion of python is great too.

One of the best courses for Probability and statistics, the course structure and syllabus was really very organized. I enjoyed completing this course.

## About the Mathematics for Data Science Specialization

Behind numerous standard models and constructions in Data Science there is mathematics that makes things work. It is important to understand it to be successful in Data Science. In this specialisation we will cover wide range of mathematical tools and see how they arise in Data Science. We will cover such crucial fields as Discrete Mathematics, Calculus, Linear Algebra and Probability. To make your experience more practical we accompany mathematics with examples and problems arising in Data Science and show how to solve them in Python.

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