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MITx: Probability - The Science of Uncertainty and Data by Edx
Build foundational knowledge of data science with this introduction to probabilistic models, including random processes and the basic elements of statistical inference -- Part of the MITx MicroMasters program in Statistics and Data Science.
Course Highlights
- The basic structure and elements of probabilistic models
- Random variables, their distributions, means, and variances
- Probabilistic calculations
- Inference methods
- Laws of large numbers and their applications
- Random processes
Skills you will learn!
Curriculum
2 Topics
Probability models and axioms
Mathematical background: Sets; sequences limits and series; (un)countable sets.
2 Topics
Conditioning and Bayes' rule
Independence
1 Topic
Counting
3 Topics
Probability mass functions and expectations
Variance; Conditioning on an event; Multiple random variables
Conditioning on a random variable; Independence of random variables
3 Topics
Probability density functions
Conditioning on an event; Multiple random variables
Conditioning on a random variable; Independence; Bayes' rule
3 Topics
Derived distributions
Sums of independent random variables; Covariance and correlation
Conditional expectation and variance revisited; Sum of a random number of independent random variables
4 Topics
Introduction to Bayesian inference
Linear models with normal noise
Least mean squares (LMS) estimation
Linear least mean squares (LLMS) estimation
3 Topics
Inequalities convergence and the Weak Law of Large Numbers
The Central Limit Theorem (CLT)
An introduction to classical statistics
3 Topics
The Bernoulli process
The Poisson process
More on the Poisson process
3 Topics
Finite-state Markov chains
Steady-state behavior of Markov chains
Absorption probabilities and expected time to absorption
MITx: Probability - The Science of Uncertainty and Data
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