Exponential Distribution
The exponential distribution is a relatively easy distribution to work with mathematically,
and it often arises in practice as being the distribution of the amount time until some
specific event occurs. For example, the amount of
Qualitative part of Systems
Dynamics to help
understand
IE2101 Introduction to
Systems Thinking
System Dynamics Part 1:
Causal Loop Diagrams
Scope
Thinking in Loops
Systems Archetypes
Examples
Thinking in Loops
Causal Loop Diagram Notation
Causal Relat
Homework 2
Question 1.
Consider the output graphs from Santa Claus workshop. Why does Desired
Production and Shipments lag behind Orders?
Figure 1a: Output Graphs from Santa Claus Workshop
Figure 1b: Stock Flow Structure of Santa Claus Workshop
Question 2
Homework
The following diagram shows the shifting the burden archetype on a countrys
reliance of foreign talents instead of building up local capability. Explain this
situation by giving examples using the different levels of perspectives (Events,
Pattern
IE2101 Introduction to
Systems Thinking
Systems Thinking
Systems Thinking
By A/P Aaron Chia
Scope
What is a System?
What is Systems Thinking?
Levels of Perspectives
Laws of the Fifth Discipline
Leverages
What is a System?
Systems, Systems, Everywhere.
Wor
IE2100 (Probability Models with Applications)
Probability
What is probability?
Here are a few interesting quotes and perspectives:
Feller, William (An Introduction to Probability Theory and its Applications)
All possible definitions of probability fall sh
IE2100 Probability Models with Applications
Semester 2 2010/20011
Course Outline
Instructors:
Dr Ng Szu Hui
Office: E1 08-09
Email: isensh@nus.edu.sg
Graduate Teaching Assistants:
Nguyen Viet Anh
Email: a0034065@nus.edu.sg
Office: ISE Ergonomics Lab
Ye Zh
Game of Monopoly
In this game, players buy, sell, rent, and trade real estate in a
cutthroat competition to bankrupt their opponents.
They take turns rolling a pair of dice, with the totals indicating how
many spaces to proceed (the game piece/token) cl
Conditional Probability, Conditional Distribution and Conditional
Expectations
In this course, we will find two very useful purposes for conditional distributions,
conditional probabilities and conditional expectations. Firstly, often in many real
situati
Discrete Time Markov Chains (DTMC)
A stochastic process cfw_X(t), tT is a time-indexed collection of random variables.
- X(t) is the sate of the process at time t
o the state space of the a stochastic process is defined as the set of all possible
values t
Discrete Time Markov Chains
Classification of States
Accessibility and Communication
Definition:
State j is accessible form state i if Pijn > 0 for some n0
Definition:
Two states i and j that are accessible to each other are said to communicate
(we write
Monty Hall Solution
At the start of the game, the a prior probability
that the prize is behind door X, P (X) = 1
3
Suppose you pick door A (arbitrary), and Monty
opens door B and shows you that there is nothing
behind door B.
Probability that Monty opens
The Poisson Process
Counting Process
Recall definition:
A stochastic process cfw_X(t), tT is a time-indexed collection of random variables.
Definition:
A stochastic process cfw_N(t), t0 is a counting process if N(t) represents the total number
of events t
Continuous Time Markov Chain (CTMC)
Recall definition:
A stochastic process cfw_X(t), tT is a time-indexed collection of random variables.
- X(t) is the state of the process at time t
o Discrete Time Stochastic Process
when set T is countable, e.g. T=cfw_
DTMC Additional Examples
Serial Production Process
A manufacturing process requires three operations, A, B and C, to be completed
sequentially.
A worker takes a raw material kit and begins operation A. The operation takes one week.
At the end of the week
Queueing Theory
Introduction
Living in this crowded world, we have to wait all the time. One of the useful areas of
application for the theory of Markovian processes is in the study of waiting lines. Queues
(waiting lines) abound in practical situations a
Homework 2 Solutions
Question 1.
Consider the output graphs from Santa Claus workshop. Why does Desired
Production and Shipments lag behind Orders?
Figure 1a: Output Graphs from Santa Claus Workshop
Figure 1b: Stock Flow Structure of Santa Claus Workshop