These notes cover “Introduction to Probability” 2nd edition by Bertsekas and Tsitsiklis
Key Takeaways
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Fundamental Concepts: The foundational ideas such as random variables, distributions, expected values, variances, and probability models were introduced. Understanding how these elements interact to describe uncertainty and randomness is essential for advanced applications.
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Bayesian vs Classical Inference: A major theme was the distinction between Bayesian inference, where parameters are treated as random variables, and classical methods, where parameters are treated as fixed but unknown constants.
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Processes and Markov Chains: We explored stochastic processes, particularly the Bernoulli and Poisson processes, and how to model them using Markov chains. These processes are widely applicable in fields like queueing theory, finance, and machine learning.
Applications
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Real-World Models: Probability models are applied in diverse fields, including risk analysis, finance, operations research, and engineering. The tools learned, from the law of large numbers to the central limit theorem, allow the analysis of complex systems.
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Statistical Inference: Bayesian and classical statistical methods are indispensable for real-world data analysis, providing tools for parameter estimation, hypothesis testing, and decision-making under uncertainty.