The course covers the axiomatic definition of probability spaces, combinatorial methods, conditional probability, random variables, distribution functions, density functions, multivariate distribution, independent random variables, functions of random variables, expected value, moments, and characteristic functions.
Students will learn about discrete and continuous probability laws, conditional probability, total probability theorem, Bayes's rule, independence, conditional independence, joint probability mass functions, expectation, variance, cumulative distribution functions, Gaussian cumulative distribution function, conditional probability density functions, joint probability density functions, moment generating functions, Markov and Chebyshev inequalities, convergence in probability, weak law of large numbers, central limit theorem, Bernoulli process, and Poisson process.
The teaching method includes lectures on various topics related to probability and random variables, with a focus on theoretical concepts and practical applications.
This course is intended for students or professionals interested in gaining a deeper understanding of probability theory and its applications in various fields such as statistics, data science, engineering, and finance.
Overview
Syllabus
Probability & Random Variables - Week 2 - Lecture 1 - Probability Spaces; Axioms and properties ...
Probability & Random Variables - Week 2 - Lecture 2 - Discrete&Continuous Prob. Laws, Conditional P..
Probability & Random Variables - Week 2 - Lecture 3 - Discrete&Continuous Prob. Laws, Conditional P..
Probability & Random Variables - Week 3 - Lecture 1 - Total Probability Theorem, Bayes's Rule.
Probability & Random Variables - Week 3 - Lecture 2 - Independence, Conditional Independence.
Probability & Random Variables - Week 3 - Lecture 3 - Independence, Conditional Independence.
Probability & Random Variables - Week 4 - Lecture 1 - Independent Trials, Counting.
Probability & Random Variables - Week 4 - Lecture 2 - Discrete Random Variables.
Probability & Random Variables - Week 4 - Lecture 3 - Discrete Random Variables.
Probability & Random Variables - Week 5 - Lecture 1 - Expectation and Variance.
Probability & Random Variables - Week 5 - Lecture 2 - Properties of Expectation&Variance, Joint PMFs.
Probability & Random Variables - Week 5 - Lecture 3 - Properties of Expectation&Variance, Joint PMFs.
Probability & Random Variables - Week 6 - Lecture 1 - Conditional PMFs.
Probability & Random Variables - Week 6 - Lecture 2 - Conditioning one random variable on another.
Probability & Random Variables - Week 6 - Lecture 3 - Conditional Expectation.
Probability & Random Variables - Week 7 - Lecture 1 - Iterated expectation, independence of rvs.
Probability & Random Variables - Week 7 - Lecture 2 - Independence of Random Variables.
Probability & Random Variables - Week 7 - Lecture 3 - Independence of Random Variables.
Probability & Random Variables - Week 8 - Lecture 1 - Continuous Random Variables.
Probability & Random Variables - Week 8 - Lecture 2 - Expectation & Cumulative Distribution Function.
Probability & Random Variables - Week 8 - Lecture 3 - Expectation & Cumulative Distribution Function.
Probability & Random Variables - Week 9 - Lecture 1 - The Gaussian CDF.
Probability & Random Variables - Week 9 - Lecture 2 - Conditional PDFs, Joint PDFs.
Probability & Random Variables - Week 9 - Lecture 3 - Conditional PDFs, Joint PDFs.
Probability & Random Variables - Week 10 - Lecture 1 - Conditioning a continuous rv on another.
Probability & Random Variables - Week 10 - Lecture 2 - Conditional PDFs, Continuous Bayes's Rule.
Probability & Random Variables - Week 10 - Lecture 3 - Conditional PDFs, Derived Distributions.
Probability & Random Variables - Week 11 - Lecture 1 - Derived Distributions.
Probability & Random Variables - Week 11 - Lecture 2 - Functions of Random Variables, Derived PDFs.
Probability & Random Variables - Week 11 - Lec. 3 - Sum of Independent rvs, Correlation & Covariance.
Probability & Random Variables - Week 12 - Lecture 1 - Applications of Covariance.
Probability & Random Variables - Week 12 - Lecture 2 - Transforms (Moment Generating Functions).
Probability & Random Variables - Week 12 - Lecture 3 - Transforms (Moment Generating Functions).
Probability & Random Variables - Week 13 - Lec. 1-Markov&Chebychev Inequalities,Convergence In Prob..
Probability & Random Variables - Week 13 - Lecture 2 - The Weak Law of Large Numbers.
Probability & Random Variables - Week 13 - Lecture 3 [Part 1] - The Central Limit Theorem.
Probability & Random Variables - Week 13 - Lecture 3 [Part 2] - The Central Limit Theorem.
Probability & Random Variables - Week 14 - Lecture 1 - The Bernoulli Process.
Probability & Random Variables - Week 14 - Lecture 2 - The Poisson Process.
Probability & Random Variables - Week 14 - Lecture 3 - The Poisson Process.
Taught by
METUopencouseware
Tags
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Reviews
4.5 rating, based on 2 Class Central reviews
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Super course really enjoyed while doing this course easily understanding easy to solve with your wonderful explanation i have learnt pleant through your course good explanations clear and easy manner
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Great experience in learning the course that helps in Signal analysis and understanding behavior of signals
