L10-09

# L10-09 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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10/6/09 Lecture 10 1 STOR 155 Introductory Statistics Lecture 10: Randomness and Probability Model The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

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10/6/09 Lecture 10 2 Let’s Make A Deal : a game show back in the 90’s. A player is given the choice of three doors. Behind one door is the Grand Prize (a car and a cruise); behind the other two doors, booby prizes (stinking pigs). The player picks a door, and the host peeks behind the doors and opens one of the rest of the doors. There is a booby prize behind the open door. The host offers the player either to stay with the door that was chosen at the beginning, or to switch to the remaining closed door. Which is better: to switch doors or to stay with the original choice? What are the chances of winning in either case? The Monty Hall Problem
10/6/09 Lecture 10 3 • Three prisoners, A, B , and C are on death row. The governor decides to pardon one of the three and chooses at random the prisoner to pardon. • He informs the warden of his choice but requests that the name be kept secret for a few days. • The next day, A tries to get the warden to tell him who had been pardoned. • The warden refuses. A then asks which of B or C will be executed. The warden thinks for a while, then tells A that B is to be executed. • Can A increase his chance of survival by swapping his fate with C ? 3 Prisoners’ Dilemma

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10/6/09 Lecture 10 4 • The previous two problems are equivalent. • Play it online at http://www.shodor.org/interactivate/activities/mont y3/ • How can we solve similar problems systematically? – Probability models Remarks
10/6/09 Lecture 10 5 • We call a phenomenon (or an experiment) random if individual outcomes are uncertain, but a regular distribution of outcomes emerges with

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## This note was uploaded on 11/17/2011 for the course STOR 155 taught by Professor Andrewb.nobel during the Fall '08 term at UNC.

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L10-09 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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