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Res.6-012 Introduction to Probability (Spring 2018, MIT OCW). Instructors: Prof. John Tsitsiklis and Prof. Patrick Jaillet.
FREE
This course includes
Hours of videos
7415 years, 11 months
Units & Quizzes
267
Unlimited Lifetime access
Access on mobile app
Certificate of Completion
The tools of probability theory, and of the related field of statistical inference, are the keys for being able to analyze and make sense of data. These tools underlie important advances in many fields, from the basic sciences to engineering and management. This resource is a companion site to 6.041SC Probabilistic Systems Analysis and Applied Probability. (from ocw.mit.edu)
Course Currilcum
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- Lecture 01.1 – Overview Unlimited
- Lecture 01.2 – Sample Space Unlimited
- Lecture 01.3 – Sample Space Examples Unlimited
- Lecture 01.4 – Probability Axioms Unlimited
- Lecture 01.5 – Simple Properties of Probabilities Unlimited
- Lecture 01.6 – More Properties of Probabilities Unlimited
- Lecture 01.7 – A Discrete Example Unlimited
- Lecture 01.8 – A Continuous Example Unlimited
- Lecture 01.9 – Countable Additivity Unlimited
- Lecture 01.10 – Interpretations and Uses of Probabilities Unlimited
- Lecture s01.0 – Overview Unlimited
- Lecture s01.1 – Sets Unlimited
- Lecture s01.2 – De Morgan’s Law Unlimited
- Lecture s01.3 – Sequences and their Limits Unlimited
- Lecture s01.4 – When does a Sequence Converge? Unlimited
- Lecture s01.5 – Infinite Series Unlimited
- Lecture s01.6 – The Geometric Series Unlimited
- Lecture s01.7 – About the Order of Summation in Series with Multiple Indices Unlimited
- Lecture s01.8 – Countable and Uncountable Sets Unlimited
- Lecture s01.9 – Proof that a Set of Real Numbers is Uncountable Unlimited
- Lecture s01.10 – Bonferroni’s Inequality Unlimited
- Lecture 03.1 – Overview Unlimited
- Lecture 03.2 – A Coin Tossing Example Unlimited
- Lecture 03.3 – Independence of Two Events Unlimited
- Lecture 03.4 – Independence of Event Complements Unlimited
- Lecture 03.5 – Conditional Independence Unlimited
- Lecture 03.6 – Independence vs Conditional Independence Unlimited
- Lecture 03.7 – Independence of a Collection of Events Unlimited
- Lecture 03.8 – Independence vs Pairwise Independence Unlimited
- Lecture 03.9 – Reliability Unlimited
- Lecture 03.10 – The King’s Sibling Unlimited
- Lecture 05.1 – Overview Unlimited
- Lecture 05.2 – Definition of Random Variables Unlimited
- Lecture 05.3 – Probability Mass Functions Unlimited
- Lecture 05.4 – Bernoulli and Indicator Random Variables Unlimited
- Lecture 05.5 – Uniform Random Variables Unlimited
- Lecture 05.6 – Binomial Random Variables Unlimited
- Lecture 05.7 – Geometric Random Variables Unlimited
- Lecture 05.8 – Expectation Unlimited
- Lecture 05.9 – Elementary Properties of Expectation Unlimited
- Lecture 05.10 – The Expected Value Rule Unlimited
- Lecture 05.11 – Linearity of Expectations Unlimited
- Lecture 05.12 – Supplement: Functions Unlimited
- Lecture 07.1 – Overview Unlimited
- Lecture 07.2 – Conditional Probability Mass Functions (PMFs) Unlimited
- Lecture 07.3 – Conditional Expectation and the Total Expectation Theorem Unlimited
- Lecture 07.4 – Independence of Random Variables Unlimited
- Lecture 07.5 – Example Unlimited
- Lecture 07.6 – Independence and Expectations Unlimited
- Lecture 07.7 – Independence, Variances and the Binomial Variance Unlimited
- Lecture 07.8 – The Hat Problem Unlimited
- Lecture 07.9 – The Inclusion-Exclusion Formula Unlimited
- Lecture 07.10 – The Variance of the Geometric Unlimited
- Lecture 07.11 – The Independence of Random Variables vs Independence of Events Unlimited
- Lecture 09.1 – Overview Unlimited
- Lecture 09.2 – Conditioning a Continuous Random Variable on an Event Unlimited
- Lecture 09.3 – Conditioning Example Unlimited
- Lecture 09.4 – Memorylessness of the Exponential Probability Density Function (PDF) Unlimited
- Lecture 09.5 – Total Probability and Expectation Theorems Unlimited
- Lecture 09.6 – Mixed Random Variables Unlimited
- Lecture 09.7 – Joint PDFs Unlimited
- Lecture 09.8 – From the Joint to the Marginal Unlimited
- Lecture 09.9 – Continuous Analogs of Various Properties Unlimited
- Lecture 09.10 – Joint CDFs Unlimited
- Lecture 09.11 – Buffon’s Needle and Monte Carlo Simulation Unlimited
- Lecture 11.1 – Overview Unlimited
- Lecture 11.2 – The PMF of a Function of a Discrete Random Variable Unlimited
- Lecture 11.3 – A Linear Function of a Continuous Random Variable Unlimited
- Lecture 11.4 – A Linear Function of a Normal Random Variable Unlimited
- Lecture 11.5 – The PDF of a General Function Unlimited
- Lecture 11.6 – The Monotonic Case Unlimited
- Lecture 11.7 – The Intuition for the Monotonic Case Unlimited
- Lecture 11.8 – A Nonmonotonic Example Unlimited
- Lecture 11.9 – The PDF of a Function of Multiple Random Variables Unlimited
- Lecture 11.10 – Simulation Unlimited
- Lecture 13.1 – Overview Unlimited
- Lecture 13.2 – Conditional Expectation as a Random Variable Unlimited
- Lecture 13.3 – The Law of Iterated Expectations Unlimited
- Lecture 13.4 – Stick-Breaking Revisited Unlimited
- Lecture 13.5 – Forecast Revisions Unlimited
- Lecture 13.6 – The Conditional Variance Unlimited
- Lecture 13.7 – Derivation of the Law of Total Variance Unlimited
- Lecture 13.8 – A Simple Example Unlimited
- Lecture 13.9 – Section Means and Variances Unlimited
- Lecture 13.10 – Mean of the Sum of a Random Number of Random Variables Unlimited
- Lecture 13.11 – Variance of the Sum of a Random Number of Random Variables Unlimited
- Lecture 13.12 – Conditional Expectation Properties Unlimited
- Lecture 14.1 – Overview Unlimited
- Lecture 14.2 – Overview of Some Application Domains Unlimited
- Lecture 14.3 – Types of Inference Problems Unlimited
- Lecture 14.4 – The Bayesian Inference Framework Unlimited
- Lecture 14.5 – Discrete Parameter, Discrete Observation Unlimited
- Lecture 14.6 – Discrete Parameter, Continuous Observation Unlimited
- Lecture 14.7 – Continuous Parameter, Continuous Observation Unlimited
- Lecture 14.8 – Inferring the Unknown Bias of a Coin and the Beta Distribution Unlimited
- Lecture 14.9 – Inferring the Unknown Bias of a Coin – Point Estimates Unlimited
- Lecture 14.10 – Summary Unlimited
- Lecture 14.11 – The Beta Formula Unlimited
- Lecture 16.1 – Overview Unlimited
- Lecture 16.2 – LMS Estimation in the Absence of Observations Unlimited
- Lecture 16.3 – LMS Estimation of One Random Variable based on Another Unlimited
- Lecture 16.4 – LMS Performance Evaluation Unlimited
- Lecture 16.5 – Example: The LMS Estimate Unlimited
- Lecture 16.6 – Example: LMS Performance Evaluation Unlimited
- Lecture 16.7 – LMS Estimation with Multiple Observations or Unknowns Unlimited
- Lecture 16.8 – Properties of the LMS Estimation Error Unlimited
- Lecture 18.1 – Overview Unlimited
- Lecture 18.2 – The Markov Inequality Unlimited
- Lecture 18.3 – The Chebyshev Inequality Unlimited
- Lecture 18.4 – The Weak Law of Large Numbers Unlimited
- Lecture 18.5 – Polling Unlimited
- Lecture 18.6 – Convergence in Probability Unlimited
- Lecture 18.7 – Convergence in Probability Examples Unlimited
- Lecture 18.8 – Related Topics Unlimited
- Lecture 18.9 – Convergence in Probability of the Sum of Two Random Variables Unlimited
- Lecture 18.10 – Jensen’s Inequality Unlimited
- Lecture 18.11 – Hoeffding’s Inequality Unlimited
- Lecture 20.1 – Overview Unlimited
- Lecture 20.2 – Overview of the Classical Statistical Framework Unlimited
- Lecture 20.3 – The Sample Mean and Some Terminology Unlimited
- Lecture 20.4 – On the Mean Squared Error of an Estimator Unlimited
- Lecture 20.5 – Confidence Intervals Unlimited
- Lecture 20.6 – Confidence Intervals for the Estimation of the Mean Unlimited
- Lecture 20.7 – Confidence Intervals for the Mean, When the Variance is Unknown Unlimited
- Lecture 20.8 – Other Natural Estimators Unlimited
- Lecture 20.9 – Maximum Likelihood Estimation Unlimited
- Lecture 20.10 – Maximum Likelihood Estimation Examples Unlimited
- Lecture 21.1 – Overview Unlimited
- Lecture 21.2 – The Bernoulli Process Unlimited
- Lecture 21.3 – Stochastic Processes Unlimited
- Lecture 21.4 – Review of Known Properties of the Bernoulli Process Unlimited
- Lecture 21.5 – The Fresh Start Property Unlimited
- Lecture 21.6 – Example: The Distribution of a Busy Period Unlimited
- Lecture 21.7 – The Time of the K-th Arrival Unlimited
- Lecture 21.8 – Merging of Bernoulli Processes Unlimited
- Lecture 21.9 – Splitting a Bernoulli Process Unlimited
- Lecture 21.10 – The Poisson Approximation to the Binomial Unlimited
- Lecture 23.1 – Overview Unlimited
- Lecture 23.2 – The Sum of Independent Poisson Random Variables Unlimited
- Lecture 23.3 – Merging Independent Poisson Processes Unlimited
- Lecture 23.4 – Where is an Arrival of the Merged Process Coming From? Unlimited
- Lecture 23.5 – The Time until the First (or Last) Lightbulb Burns Out Unlimited
- Lecture 23.6 – Splitting a Poisson Process Unlimited
- Lecture 23.7 – Random Incidence in the Poisson Process Unlimited
- Lecture 23.8 – Random Incidence in a Non-Poisson Process Unlimited
- Lecture 23.9 – Different Sampling Methods can Give Different Results Unlimited
- Lecture 23.10 – Poisson vs Normal Approximations to the Binomial Unlimited
- Lecture 23.11 – Poisson Arrivals during an Exponential Interval Unlimited
- Lecture 25.1 – Brief Introduction Unlimited
- Lecture 25.2 – Overview Unlimited
- Lecture 25.3 – Markov Chain Review Unlimited
- Lecture 25.4 – The Probability of a Path Unlimited
- Lecture 25.5 – Recurrent and Transient States: Review Unlimited
- Lecture 25.6 – Periodic States Unlimited
- Lecture 25.7 – Steady-State Probabilities and Convergence Unlimited
- Lecture 25.8 – A Numerical Example – Part II Unlimited
- Lecture 25.9 – Visit Frequency Interpretation of Steady-State Probabilities Unlimited
- Lecture 25.10 – Birth-Death Processes, Part I Unlimited
- Lecture 25.11 – Birth-Death Processes, Part II Unlimited
