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Online Course

# Introduction to Stochastic Processes

8
Found in
9 Months, Online Machine Learning & AI Diploma Columbia Engineering Executive Education via EMERITUS AD

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## Overview

Random is a common thing that we came across in our daily life. Questions like how much traffic will be on my route today? how much I need to wait to catch a bus to my workplace? will I gain or lose money in stock market? may not have fixed answer as they are associated with random events. In this course we will learn various probability techniques to model a random events and study how to analyze them.

INTENDED AUDIENCE : All disciplines learners PRE-REQUISITE : Introductory real analysis SUPPORT INDUSTRY : This is a basic course. All companies will recognize

## Syllabus

COURSE LAYOUT Week 1: Introductions to events, probability, conditional probability, Bayes rule Week 2: Random Varaibles, Expectations, Variance, Various type of distributions Week 3: CDF and PDF of random variables. Conditional CDF and PDFs Week 4: Jointly distributed random variables, covariance and independence Week 5: Transformation of random variables and their distributions Week 6: Introductions to Random processes. Stationary and Ergodicity Week 7: Convergence of Sequence of RVs. (almost surely, in probability, in distributions). Week 8: Strong and weak law of large numbers, central limit theorem Week 9: Discrete Markov chains. Stopping time and Strong Markov property Classification of Transient and Recurrent states Week 10: Counting Process, Poisson Processes and its applications Week 11: Renewal Theory. Elementary and Renewal Reward Theorem and Week 12: Introduction to Continuous Markov Chains

#### Taught by

Prof. Manjesh hanawal

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