INFM 718A / LBSC 705 Information For Decision Making

1
INFM 718A / LBSC 705 Information For Decision
Making

• Lecture 6

2
Overview

• Networks
• Transportation/Shipment/Assignment
• Maximum Flow
• Shortest Path
• Examples from textbook ? In-class exercises
• Probability

3
Shortest Path

• Textbook example pp. 152-157

4
Shortest Path
12
5
2
7
7
1
4
3
15
6
1
4
9
7
3
2
3
3
10
8
6
5
6
5
Shortest Path

• f(9) 0
• f(8) 10
• f(7) 3
• f(6) 16
• f(5) 10

6
Shortest Path

• f(4) min f(8) 7 17
• f(7) 15 18
• f(6) 3 19
• f(5) 4 14 14

7
In-Class Exercises 3

• Transportation/Shipment/Assignment
• Question 1
• Question 4
• Maximum Flow
• Question 2
• Question 5
• Shortest Path
• Question 3
• Question 6

8
Probability

• Likelihood that an outcome will occur when the
  uncertainty related to it is resolved.
• We are interested in objective uncertainty in
  this lecture.
• Outcomes need to be mutually exclusive and
  collectively exhaustive.

9
Probability
10
Examples

• Flipping a coin 2 possible outcomes (heads or
  tails), with equal likelihoods, each with a
  probability of 1/2.
• Throwing a die 6 possible outcomes (1,2, 3, 4,
  5, 6), with equal likelihoods, each with a
  probability of 1/6.
• P (even) 1/2
• P (gt2) 4/6

11
Disjoint and Independent Events

• Disjoint events Two (or more) events with no
  common outcomes. E.g. P (2 and odd).
• Independent events Two (or more) events, where
  knowing the outcome of one event will not provide
  any information about the probability of the
  other event. E.g. Throwing a die and flipping a
  coin together.

12
Joint Probability

• Probability that two independent events will
  occur together. E.g. Throw a dice, flip a coin,
  what is the probability that the die shows 1 and
  the coin shows heads. P (1 and H) 1/6 1/2
  1/12

13
Conditional Probability

• Probability of an outcome, under the condition
  that another, dependent event has had a certain
  outcome. E.g. Probability that the die shows 1,
  based on the information that it shows an odd
  number. P (1 odd).

14
Bayes Theorem
15
In-Class Exercises 4

• Probability