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Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video Based |
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIT Kanpur |
The Syllabus
- Introduction to the course: A review of basic Probability and Measure Theoretic integration
- Lp spaces (definition, properties as a Banach space, dual space)
- Independence of Events and Random variables, Borel-Cantelli Lemma (second half)
- Product measures (construction, integration, Fubini-Tonelli Theorem)
- Almost sure convergence of sequences of Random variables (definition and examples)
- Other modes of convergence of sequences of Random variables (convergence in probability, convergence in p-th mean, definition and examples)
- Relations between various modes of convergence (examples and counter-examples)
- Properties of various modes of convergence
- Almost sure convergence of series of Random variables (Kolmogorov’s inequality)
- Almost sure convergence of series of Random variables – continued (Kolmogorov’s Three series Theorem)
- Law of Large numbers (Khinchin’s Weak law, Kolmogorov’s Strong law, applications)
- Characteristic Functions (properties, Inversion formulae)
- Weak convergence or convergence in distribution (definition and examples)
- Equivalent conditions or formulations of weak convergence (Helly-Bray Theorem, Portmanteau Lemma, Levy’s Continuity Theorem)
- Equivalent conditions or formulations of weak convergence – continued
- Central Limit Theorem (Lindeberg-Levy CLT)
- Central Limit Theorems (Lindeberg-Feller CLT, Lyapunov CLT)
- Applications
- Slutky’s Theorem, Delta Method, Comments on Glivenko-Cantelli Theorem and Berry-Esseen Theorem
- Conclusion of the course
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