IE 332 • Tüm Sınavlar • Mathematical Modeling and Optimization III
TED Üniversitesi IE 332 (Mathematical Modeling and Optimization III) Midterm sınavına hazırlık paketi.
İşlenen konular: Discrete Time Markov Chains, Steady-State Distribution and Classification of States, Long Term Properties of Markov Chains, Absorbing Markov Chains, Poisson Processes.
Ayda 932 TL, peşin fiyatına 3 taksit
Eğitmen
Ömer Faruk Altun
Co-founder & Head of Education
2011 yılında Endüstri Mühendisliği okumak için başladığım Sabancı Üniversitesi'nden 2018 yılında Bilgisayar Mühendisi olarak mezun oldum. 13 yıldır Altun ismiyle başta Sabancı Üniversitesi olmak üzere çeşitli okullarda Endüstri ve Bilgisayar Mühendisliği alanlarında ders vermekteyim. Unicourse'ta sunduğum derslerin yanında eğitim departmanının da sorumluluğunu üstlenmekteyim.
Konular
Probability Review (İzlemeden Başlama)
4 konu anlatımı
Random Variables and Probability Distributions
Conditional Probability
Total Probability Rule
Expected Value
Discrete Time Markov Chains
8 konu anlatımı
What is a Markov Chain?
One-Step Transition Probabilities
Example
n-Step Transition Probabilities
Chapman-Kolmogorov Equations
Example
Unconditional State Probabilities
Example
Steady-State Distribution and Classification of States
7 konu anlatımı
Steady State Distribution
Example
Classes and State Properties
Periodicity and Ergodic Markov Chains
Example
Example
Example
Long Term Properties of Markov Chains
5 konu anlatımı
First Passage Times
Example
Expected First Passage Time
Expected Recurrence Time
Example
Absorbing Markov Chains
9 konu anlatımı
Absorbing Markov Chains
Matrix Structure
Inverse of a Matrix
Expected Number of State Visits
Example
Expected Time Until Absoption
Example
Absorption Probabilities
Example
Poisson Processes
11 konu anlatımı
Counting Processes
Assumptions of Poisson Processes
Example 1
Memoryless Property
Example 2
Minimum of Exponential Random Variables
Example 3
Thinning
Example 4
Superposition
Example 5
Sample Midterm Problems
19 soru
Discrete Time Markov Chains 1
Discrete Time Markov Chains 2
Discrete Time Markov Chains 3
Discrete Time Markov Chains 4
Limiting Distribution and State Classifications 1
Limiting Distribution and State Classifications 2
Limiting Distribution and State Classifications 3
Limiting Distribution and State Classifications 4
Limiting Distribution and State Classifications 5
Limiting Distribution and State Classifications 6
Limiting Distribution and State Classifications 7
Long Term Properties of Markov Chains 1
Long Term Properties of Markov Chains 2
Absorbing Markov Chains 1
Absorbing Markov Chains 2
Poisson Processes 1
Poisson Processes 2
Poisson Processes 3
Poisson Processes 4
Birth-and-Death Processes
15 konu anlatımı
Continuous Time Markov Chains
Example 1
Example 2
Steady State Distribution
Birth and Death Processes
Random Rates, Finite Chain
Example 3
Random Rates, Infinite Chain
Example 4
Equal Rates, Infinite Chain, Single Server
Example 5
Equal Rates, Finite Chain, Single Server
Example 6
Equal Rates, Finite Chain, Multiple Servers
Example 7
Queueing Theory
10 konu anlatımı
Kendall's Notation
Terminology
M/M/1 Queue
Example 1
M/M/s Queue
Example 2
M/M/1/K Queue
Example 3
M/M/s/K Queue
Example 4
Deterministic Dynamic Programming (Hatırlatma)
5 konu anlatımı
A New Approach to Optimization Problems
Inventory Problems
Example 1
Resource Allocation Problems
Example 2
Probabilistic Dynamic Programming
4 konu anlatımı
What is it?
Example 1
Example 2
Example 3
Markov Decision Processes
6 konu anlatımı
Introduction
Policy Improvement Algorithm: Step 1
Policy Improvement Algorithm: Step 2
Example 1
LP Solution
LP Solution with Discount
Sample Final Problems
19 soru
Birth and Death 1
Birth and Death 2
Birth and Death 3
Birth and Death 4
Queueing Theory 1
Queueing Theory 2
Queueing Theory 3
Queueing Theory 4
Queueing Theory 5
Queueing Theory 6
Queueing Theory 7
Queueing Theory 8
Probabilistic Dynamic Programming 1
Probabilistic Dynamic Programming 2
Probabilistic Dynamic Programming 3
Probabilistic Dynamic Programming 4
Probabilistic Dynamic Programming 5
Probabilistic Dynamic Programming 6
Markov Decision Process 1