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 2 1 6 5 4 3 9 8 7 1 2 6 3 12 7 315 10 4 7 56 3

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 (>2) = 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