IE 3554 • Midterm • Stochastic Operations Research

Random Variables and Probability Distributions

Conditional Probability

Total Probability Rule

Expected Value

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

Example

Classes and State Properties

Periodicity and Ergodic Markov Chains

Example

Example

Example

First Passage Times

Example

Expected First Passage Time

Expected Recurrence Time

Example

What is an Absorbing MC?

Absorption Probabilities

Example

Probability of Ever Visiting a State

Example

Expected Number of State Visits

Example

Expected Time Until Absoption

Example

Discrete Time Markov Chains 1

Discrete Time Markov Chains 2

Discrete Time Markov Chains 3

Discrete Time Markov Chains 4

Discrete Time Markov Chains 5

Discrete Time Markov Chains 6

Classification of States and Steady-state Analysis 1

Classification of States and Steady-state Analysis 2

Classification of States and Steady-state Analysis 3

Classification of States and Steady-state Analysis 4

Classification of States and Steady-state Analysis 5

Classification of States and Steady-state Analysis 6

First Step Analysis and Absorbing Chains 1

First Step Analysis and Absorbing Chains 2

First Step Analysis and Absorbing Chains 3

First Step Analysis and Absorbing Chains 4