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Probability Theory, Statistics and Exploratory Data Analysis

Approx. 22 hours to complete

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Course Summary

This course provides an introduction to probability theory and statistics, covering topics such as random variables, probability distributions, hypothesis testing, and regression analysis.

Key Learning Points

Gain a solid foundation in probability theory and statistics
Learn how to analyze and interpret data
Develop skills in hypothesis testing and regression analysis

Job Positions & Salaries of people who have taken this course might have

Statistician
- USA: $72,000
- India: ₹4,80,000
- Spain: €28,000
Data Analyst
- USA: $62,000
- India: ₹4,20,000
- Spain: €24,000
Actuary
- USA: $97,000
- India: ₹6,60,000
- Spain: €38,000

Learning Outcomes

Develop a strong foundation in probability theory and statistics
Gain practical skills in data analysis and interpretation
Learn how to use statistical models to make informed decisions

Prerequisites or good to have knowledge before taking this course

Basic understanding of algebra and calculus
Familiarity with basic statistics concepts

Course Difficulty Level

Intermediate

Course Format

Online self-paced course
Video lectures and quizzes
Peer-graded assignments

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Description

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.

The core concept of the course is random variable — i.e. variable whose values are determined by random experiment. Random variables are used as a model for data generation processes we want to study. Properties of the data are deeply linked to the corresponding properties of random variables, such as expected value, variance and correlations. Dependencies between random variables are crucial factor that allows us to predict unknown quantities based on known values, which forms the basis of supervised machine learning. We begin with the notion of independent events and conditional probability, then introduce two main classes of random variables: discrete and continuous and study their properties. Finally, we learn different types of data and their connection with random variables. While introducing you to the theory, we'll pay special attention to practical aspects for working with probabilities, sampling, data analysis, and data visualization in Python. This course requires basic knowledge in Discrete mathematics (combinatorics) and calculus (derivatives, integrals). This Course is part of HSE University Master of Data Science degree program. Learn more about the admission into the program and how your Coursera work can be leveraged if accepted into the program here https://inlnk.ru/rj64e.

Outline

Conditional probability and Independence
Introduction to the 1st week
Conditional probability. Motivation and Example
Conditional probability. Definition
Independent events. Example
Independent events. Definition
Mosaic Plot. Visualization of conditional probabilities and Independence
Using independence to find probabilities. Examples
Pairwise and mutual independence
Bernoulli Scheme
Law of total probability
Bayes's rule
Python for conditional probabilities
Conditional probability. Highlights
About University
Rules on the academic integrity in the course
Coins, dices and conditional probability
Independence and intersection
Fair coin and independence
Mutual independence conditions
Call center total probability
Bayes's taxi companies
Rare disease paradox

Random variables
Introduction to the 2nd week
Examples of random variables
Mathematical definition of random variable
Probability distribution and probability mass function (PMF)
Binomial distribution
Expected value of random variable. Motivation and definition
Expected value example and calculation
Expected value as best prediction
Variance of random variable. Motivation and definition
Discrete random variables with infinite number of values
Saint Petersburg Paradox. Example of infinite expected value
Geometric and Poisson distributions
Generating discrete random variables with Python
Numpy, scipy and matplotlib for generation and visualization of common distributions
Random variables. Highlights
Expected value exercises
Variance skill test
Random variables and geometric series

Systems of random variables; properties of expectation and variance, covariance and correlation.
Introduction to the 3rd week
Linear transformations of random variables
Linearity of expected value
Symmetric distributions and their expected values
Functions of random variables
Properties of variance
Sum of random variables. Expected value and variance
Joint probability distribution
Marginal distribution
Independent random variables
Another example of non-independent random variables
Expected value of product of independent random variables
Variance of sum of random variables. Covariance
Properties of covariance
Correlation of two random variables
Systems of random variables. Highlights
PMF of linear transformations
Expectation properties
Joint distribution skill test
Joint PMF
Variance of Binomial random variable
Covariance for a dice roll
Correlation quiz

Continuous random variables
Introduction to the 4th week
Continuous random variables. Motivation and Example
Probability density function (PDF)
Cumulative distribution function (CDF)
Properties of CDF
Linking PDF and CDF
Examples of probability density functions
Histogram as approximation to a graph of PDF
Expected value of continuous random variable
Variance of continuous random variable. Properties of expected value and variance
Transformations of continuous random variables and their PDFs
Joint CDF and PDF. Level charts. Marginal PDF
Independence, covariance and correlation of continuous random variables
Mixed random variables. Example
Generating and visualizing continuous random variables with Python
Generating correlated random variables with Python
CDF of discrete random variable
PDF and CDF skill test
Finding expectation with PDF
Finding variance with PDF
Expectation of a function of random variable
PDF skill test
Variance of sum of Gaussian random variables
Distinguishing random variables

From random variables to statistical data. Data summarization and descriptive statistics.
Introduction to the 5th week
Basic statistical model
Variable types in statistics. Conversion of categorical variables to numeric
Measures of central tendency. Average, median and mode
Measures of statistical dispersion. Sample variance, quartiles and interquartile range
Distribution visualization. Histograms and bar plots
Descriptive statistics of sample vs population
Descriptive statistics in Pandas
Basic visualizations of statistical data in Python
Converting columns in dataframes
Data summarization and descriprive statistics. Highlights
Variable types practice
Measures of central tendency
Sample variance
Data visualizations

Correlations and visualizations
Introduction to the 6th week
Two numeric variables. Scatter plot and levels of population's joint PDF
Sample covariance and Pearson's correlation
Correlation vs causation
Rank correlations for non-linearly dependent data and ordered categorical data
Finding correlations in Pandas
Correlations and visualizations. Highlights
Course summary. What's next?
Correlation and causation
Correlation urban legends
Final project

Summary of User Reviews

Discover the world of probability and statistics with this online course from Coursera. Students praise the course for its depth and comprehensiveness, and appreciate the real-world examples that make the content easy to understand.

Key Aspect Users Liked About This Course

Real-world examples that make the content easy to understand

Pros from User Reviews

Comprehensive coverage of probability and statistics
Excellent use of real-world examples
Engaging and knowledgeable instructors
Well-structured course material
Great for beginners and advanced learners alike

Cons from User Reviews

Some users find the course challenging
Limited interaction with instructors
Some users feel the course is too theoretical
Occasional technical issues with the platform
No certificate of completion for free users

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