About this Course

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100% online
Start instantly and learn at your own schedule.
Flexible deadlines
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Approx. 19 hours to complete


Shareable Certificate
Earn a Certificate upon completion
100% online
Start instantly and learn at your own schedule.
Flexible deadlines
Reset deadlines in accordance to your schedule.
Approx. 19 hours to complete

Offered by


National Research University Higher School of Economics

Start working towards your Master's degree

This course is part of the 100% online Master of Data Science from National Research University Higher School of Economics. If you are admitted to the full program, your courses count towards your degree learning.

Syllabus - What you will learn from this course


Week 1

3 hours to complete

Conditional probability and Independence

3 hours to complete
13 videos (Total 123 min), 1 reading, 7 quizzes
13 videos
Conditional probability. Motivation and Example13m
Conditional probability. Definition8m
Independent events. Example7m
Independent events. Definition12m
Mosaic Plot. Visualization of conditional probabilities and Independence11m
Using independence to find probabilities. Examples10m
Pairwise and mutual independence12m
Bernoulli Scheme11m
Law of total probability14m
Bayes's rule4m
Python for conditional probabilities9m
Conditional probability. Highlights3m
1 reading
Rules on the academic integrity in the course10m
7 practice exercises
Coins, dices and conditional probability20m
Independence and intersection5m
Fair coin and independence6m
Mutual independence conditions5m
Call center total probability5m
Bayes's taxi companies5m
Rare disease paradox5m

Week 2

3 hours to complete

Random variables

3 hours to complete
15 videos (Total 150 min)
15 videos
Examples of random variables11m
Mathematical definition of random variable5m
Probability distribution and probability mass function (PMF)15m
Binomial distribution10m
Expected value of random variable. Motivation and definition14m
Expected value example and calculation11m
Expected value as best prediction15m
Variance of random variable. Motivation and definition7m
Discrete random variables with infinite number of values11m
Saint Petersburg Paradox. Example of infinite expected value6m
Geometric and Poisson distributions6m
Generating discrete random variables with Python11m
Numpy, scipy and matplotlib for generation and visualization of common distributions12m
Random variables. Highlights3m
3 practice exercises
Expected value exercises20m
Variance skill test25m
Random variables and geometric series10m

Week 3

3 hours to complete

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

3 hours to complete
16 videos (Total 127 min)
16 videos
Linear transformations of random variables8m
Linearity of expected value6m
Symmetric distributions and their expected values6m
Functions of random variables5m
Properties of variance6m
Sum of random variables. Expected value and variance8m
Joint probability distribution12m
Marginal distribution8m
Independent random variables7m
Another example of non-independent random variables8m
Expected value of product of independent random variables8m
Variance of sum of random variables. Covariance11m
Properties of covariance10m
Correlation of two random variables7m
Systems of random variables. Highlights3m
7 practice exercises
PMF of linear transformations5m
Expectation properties5m
Joint distribution skill test15m
Joint PMF10m
Variance of Binomial random variable5m
Covariance for a dice roll5m
Correlation quiz5m

Week 4

3 hours to complete

Continuous random variables

3 hours to complete
16 videos (Total 156 min)
16 videos
Continuous random variables. Motivation and Example10m
Probability density function (PDF)9m
Cumulative distribution function (CDF)13m
Properties of CDF6m
Linking PDF and CDF11m
Examples of probability density functions10m
Histogram as approximation to a graph of PDF11m
Expected value of continuous random variable9m
Variance of continuous random variable. Properties of expected value and variance7m
Transformations of continuous random variables and their PDFs11m
Joint CDF and PDF. Level charts. Marginal PDF10m
Independence, covariance and correlation of continuous random variables9m
Mixed random variables. Example11m
Generating and visualizing continuous random variables with Python10m
Generating correlated random variables with Python11m
8 practice exercises
CDF of discrete random variable7m
PDF and CDF skill test15m
Finding expectation with PDF5m
Finding variance with PDF5m
Expectation of a function of random variable2m
PDF skill test7m
Variance of sum of Gaussian random variables5m
Distinguishing random variables3m



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About the Mathematics for Data Science Specialization

Mathematics for Data Science

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