Introduction to probability. Random variables and its distribution. Expectation, moments and moment generating functions. Conditional probability and expectations. Transformations of random variables, and order statistics. Stochastic convergence and central limit theorem. Sampling distribution. Point estimation, method of moments and maximum likelihood. Large and small sample properties. Sufficiency. Interval estimation. Testing of hypotheses - MP, UMP, UMPU, GLR, LM and Wald tests.
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| Dönem | Course CPA | |
|---|---|---|
| 2025-2026 Fall | 2.87 | 1 sec · 19 öğr |
| 2024-2025 Fall | 2.65 | 1 sec · 23 öğr |
| 2023-2024 Fall | 2.74 | 1 sec · 13 öğr |
| 2022-2023 Fall | 2.78 | 1 sec · 20 öğr |
| 2021-2022 Fall | 3.32 | 1 sec · 14 öğr |
| 2020-2021 Fall | 3.25 | 1 sec · 17 öğr |
| 2019-2020 Fall | 2.73 | 1 sec · 19 öğr |
| 2018-2019 Fall | 2.59 | 1 sec · 19 öğr |
| 2017-2018 Fall | 2.79 | 1 sec · 18 öğr |
| 2016-2017 Fall | 1.82 | 1 sec · 22 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.
Course Learning Outcomes: Course Learning Outcome Assessment Students can formally define fundamental statistical concepts by using tools from set theory and probability theory. (K1) Midterm Final Quizzes Students can derive the moment generating functions and the first two moments for standard distribution functions. (K1) Midterm Final Quizzes Students can correctly explain the theoretical details of different types of asymptotic convergence and compare these formally. (K1) Midterm Final Quizze
Sample space, events, axioms. Basics of probability theory. Conditional probability, independence. Distribution and density functions. Some common discrete and continous distributions and their basic moments. Functions of random variables, transformations. Expected value, other moments, moment generating functions. Cumulant generating and characteristic functions. Law of iterated expectations, hierarchical models. Multivariate random variables, covariance, correlation. Basic notions, stochastic orders of magnitude. Convergence in probability, almost sure convergence, other convergence concepts. Law of large numbers, central limit theorem. Maximum likelihood method. Properties of the likelihood function, information equality, score function. Basic asymptotic expansions, asymptotic distribution of likelihood estimators. Likelihood vs quasi-likelihood. Method of moments, asymptotics of moment estimators, generalised method of moments. ECTS - Workload Table: Activities Number Hours Workload Laboratory (including preparation) 14 1 14 Course hours 14 3 42 Quiz 8 ,25 2 Preparation for Midterm exam 1 30 30 Final exam 1 3 3 Midterm exam 1 2 2 Preparation for Final exam 1 50 50 Preparation for Quiz 8 1 8 Total Workload: 151 Total Workload / 30: 151 / 30 5.03 ECTS Credits of the Course: 5 Type of Course: Lecture