Info3010, Week 7 notes
Info3010, Week 7 notes Info3010
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This 7 page Class Notes was uploaded by Rebecca Evans on Monday February 29, 2016. The Class Notes belongs to Info3010 at Tulane University taught by Srinivas Krishnamoorthy in Spring 2016. Since its upload, it has received 28 views. For similar materials see Business Modeling in Business at Tulane University.
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Date Created: 02/29/16
Probabilistic Modeling Not use excel Probability: tells us the likelihood of an outcome 3 rules Probability between 0 and 1 If a set of outcomes are mutually exclusive and collectively exhausted then the sum of probability is 1 Mutually exclusive: if two outcomes cannot happen at the same time Collectively Exhaustive: set of outcomes encompasses the entire range of possible outcomes Example: outcome of a game between Red Sox and Yankees R=Red Sox win Y=Yankees win R and Y are mutually exclusive (both cannot happen at same time) and collective exhaustive (together probability is 1) P(Red Sox win or Yankees win) = P(R or Y) = P(R) + P(Y) = 1 Independent: the outcome of one event does not affect the probability of the outcome of the other event H=will Paris Hilton get married? S=Will Srini find love? P(H and S)= P(H) x P(S) Decision Trees: model used for decision making in chance environments (like gambling, movie business, sports plays, startup business Sequence of decisions and random events ------ Arcs or “branches” o Events/ random events Square=decisions ##’s’ =final outcomes/leaves Expected value=long term average Example: potential box office earning of Hollywood moviebetter outcome (great profit) is least likely and lowest outcome is most probablehighly risky business Expected revenue=sum of probability*outcome =(.1)($200)+(.4) ($30)+(.5)($10) Hollywood example Probability Outcome .1 $200M .4 $30M .5 $10M Expected Value and Rollback *see handwritten notes Risk and Return Hollywood Example: Expected value=$2M Amount Invested=$35M % return=$2M/35M= approximately 5-6% 90% chance of loss (.4+.5) System of investing in risky business (movies, start- up)=promote creativity; individual=bad because probably not have good return Chance Environment Outcome=skill + luck Tactics: o Take the chances that have a positive EV o Increase the number of chances taken o Reducing/manage the costs of each chance Fallacies and Laws Fallacy of Small Numbers: o When sample size is small-outcomes do not always reflect “potential” Law of Large Numbers o Outcome begins to match “potential” as the sample size grows February 24: Sharapova Sportswear & Matthew Magnate 1) The Sharapova Sportswear Company has designed two new tennis skirt styles for next year, “Wimbledon” and “Flushing Meadows”. The company can produce either or both or neither of the two styles. Thus, management must select one of four actions available: (a) “Wimbledon” only, (b) “Flushing Meadows” only, (c) both, or (d) neither. The cost of production, all of which must be borne in advance if a model design is to be produced, is $50,000 for either of the models, but it is $125,000 for both together because of the strain in capacity involved in producing two styles. The profit including all income and costs except production cost, is $100,000 per style if the style is successful, and zero if the style is unsuccessful. If only one skirt style is produced then it has a 40% chance of being commercially successful. If both styles are produced then there is a 16% chance that both of them are successful, a 24% chance that only “Wimbledon” is successful and a 24% chance that only “Flushing Meadows” is successful. (a) Draw a decision tree to help the Sharapova Company with the production decision. Assuming that the company wants to maximize expected value of profits, what is the best course of action? 2) Mathew Magnate Matthew Magnate plans to open two casinos - one in Detroit and one in Windsor. He has to submit proposals to the gaming boards of each of the two cities. The probability of a casino being approved by a board is 0.30 and completely independent of the approval outcome of the other casino (since the decisions are being made by different boards). Each casino will generate $4 billion in profit if it is opened after approval. If a casino is not approved, then profits from that casino will be $0. If both the casinos are approved and opened then total profits will be $6 billion (because the two casinos will eat into each other’s business). Assume that Matthew will definitely open a casino if it is approved. What is the expected value of profits from submitting the two proposals? February 26: Clouseau Classification 1) Chief Inspector Clouseau has an uncanny way of detecting criminals and innocent people. He can sniff and identify if a criminal is a criminal with an accuracy of 97%. He can also sniff and identify if an innocent person is innocent with an accuracy of 94%. In other words, if Chief Inspector Clouseau sniffs a criminal then 97% of the time he will classify him as a criminal, and if he sniffs an innocent person then 94% of the time he will classify him as innocent. Chief Inspector Clouseau lives in the town of Saint Amand Montrond which has 1,000 inhabitants, out of which it is known that 150 are criminals. However, nobody knows who these 150 are. A person has been brought in for questioning and Chief Inspector Clouseau has been called upon to perform his sniff test. a) Draw the decision tree corresponding to the process of Chief Inspector Clouseau classifying the person. b) What is the probability that Chief Inspector Clouseau classifies the person as a criminal? c) If Chief Inspector Clouseau classifies the person as a criminal then what is the probability that the person really is a criminal?
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