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IE 523

Probabilistic Analysis

IE 523 rebuilds probability from the ground up on measure-theoretic foundations, treating sigma-algebras as information structures and random variables as measurable functions rather than the recipe-driven objects you met in undergrad probability. Expect eleven problem sets that push you through Lebesgue integration, Radon-Nikodym, product measures, conditional expectation, and the convergence theorems that culminate in the laws of large numbers and the CLT. This is the gateway course for serious stochastic work in the IE PhD track — anything involving martingales, Markov processes, or rigorous statistics downstream assumes you can think fluently in this language.

Credit3ECTS5FacultyFaculty of EngineeringBölümIndustrial EngineeringMüfredatY4 Bahar

Değerlendirme 30% — 1 adım

30%
Homework Each homework is worth 3%. Your lowest homework grade will be dropped. 30%

Önerilen kaynaklar 2 kitap

📖
Önerilen
Probability and Stochastics
Erhan Çınlar
2011 · Springer
📖
Önerilen
A Probability Path
Sidney I. Resnick
Reprint of 2005 edition · Birkhäuser

Haftalık müfredat 14 hafta

Hafta 1
What is probability theory about? Random experiments, sigma-algebras, measurable spaces, Borel sigma-algebra.
Hafta 2
Dynkin systems, pi systems, monotone class theorem for sets.
Hafta 3
Probability and measure spaces, properties of measures, constructing measures, Lebesgue measure.
Hafta 4
Random variables, measurable functions, generated sigma-algebras.
Hafta 5
Expectations, Lebesgue integrals, properties and limit theorems.
Hafta 6
Distributions of random variables, integral transformations, Radon-Nikodym theorem.
Hafta 7
Discrete and continuous random variables, Laplace and Fourier transforms, cumulative distribution functions, quantiles.
Hafta 8
Product sigma-algebras, random vectors, transition kernels.
Hafta 9
Product measures, Fubini and Tonelli theorems.
Hafta 10
Independence, Gaussian vectors.
Hafta 11
Conditional expectations.
Hafta 12
Conditional probabilities, conditional distributions, infinite product spaces, Ionescu Tulcea theorem, Bernoulli processes.
Hafta 13
Almost sure convergence, convergence in probability, L^p spaces, convergence in L^p.
Hafta 14
Law of large numbers, weak convergence, central limit theorem.

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Geçmiş GPA dağılımı 19 dönem · ort. 3.02

DönemCourse CPA
2025-2026 Fall 3.30 1 sec · 16 öğr
2024-2025 Fall 3.26 1 sec · 21 öğr
2023-2024 Fall 2.97 1 sec · 22 öğr
2022-2023 Fall 3.00 1 sec · 15 öğr
2021-2022 Fall 3.46 1 sec · 10 öğr
2020-2021 Fall 3.11 1 sec · 23 öğr
2019-2020 Fall 3.40 1 sec · 24 öğr
2018-2019 Fall 3.07 1 sec · 14 öğr
2017-2018 Fall 3.25 1 sec · 19 öğr
2016-2017 Fall 3.13 1 sec · 32 öğr

Aggregate course GPA — Bilkent STARS'tan public data. Hoca-bazlı per-section detayı için STARS evaluation report →. Öğrenci anket cevapları KVKK kapsamında defter'de tutulmaz.

⚠️ FZ engelleyen şartlar

To be able to take the final exam, you must collect at least 15 out of 30 in the homework assignments.

Hocalar 0 bu dönem · 6 geçmiş

Geçmişte ders veren (6 kişi)
Çağın Ararat, Ülkü Gürler, Savaş Dayanık, Mehmet Murat Fadıloğlu, Vladimir V. Anisimov, S. Kambo