Unit 8: Limit theorems and classical statistics Linear least mean squares (LLMS) estimation.Conditional expectation and variance revisited Sum of a random number of independent random variables.Sums of independent random variables Covariance and correlation.Unit 6: Further topics on random variables Conditioning on a random variable Independence Bayes' rule.Conditioning on an event Multiple random variables.Conditioning on a random variable Independence of random variables.Variance Conditioning on an event Multiple random variables.Probability mass functions and expectations.Mathematical background: Sets sequences, limits, and series (un)countable sets.To learn more about this program, please visit. You will complete this course and three others from MITx, at a similar pace and level of rigor as an on-campus course at MIT, and then take a virtually-proctored exam to earn your MicroMasters, an academic credential that will demonstrate your proficiency in data science or accelerate your path towards an MIT PhD or a Master's at other universities. Master the skills needed to be an informed and effective practitioner of data science. This course is part of the MITx MicroMasters Program in Statistics and Data Science. It is a challenging class but will enable you to apply the tools of probability theory to real-world applications or to your research. The contents of this courseare heavily based upon the corresponding MIT class - Introduction to Probability - a course that has been offered and continuously refined over more than 50 years. an introduction to random processes (Poisson processes and Markov chains).the main tools of Bayesian inference methods.multiple discrete or continuous random variables, expectations, and conditional distributions.The course covers all of the basic probability concepts, including: Furthermore, while the applications are multiple and evident, we emphasize the basic concepts and methodologies that are universally applicable. But instead of relying on the traditional "theorem-proof" format, we develop the material in an intuitive - but still rigorous and mathematically-precise - manner. Probabilistic models use the language of mathematics. Probabilistic modeling and the related field of statistical inference are the keys to analyzing data and making scientifically sound predictions. The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications.
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