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CX4240 HOMEWORK 1 LE SONG

CX4240 HOMEWORK 1 LE SONG

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Author: Christine Farr
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CX4240 Homework 1Le SongDeadline: 2/06 Thur, 9:30am (before starting the class)• Submit your answers as an electronic copy on T-square.• No unapproved extension of deadline is allowed. Late submission will lead to 0 credit.• Typing with Latex is highly recommended. Typing with MS Word is also okay. If you handwrite, tryto be clear as much as possible. No credit may be given to unreadable handwriting.• Explicitly mention your collaborators if any.1ProbabilityOn the morning of September 31, 1982, the won-lost records of the three leading baseball teams in thewestern division of the National League of the United States were as follows:TeamAtlanta BravesSan Francisco GiantsLos Angeles DodgersWon878686Lost727373Each team had 3 games remaining to be played. All 3 of the Giants games were with the Dodgers, andthe 3 remaining games of the Braves were against the San Diego Padres. Suppose that the outcomes of allremaining games are independent and each game is equally likely to be won by either participant. If twoteams tie for first place, they have a playoff game, which each team has an equal chance of winning.(a) What is the probability that Atlanta Braves wins the division? [5 pts](b) What is the probability that San Francisco Giants wins the division? [5 pts](c) What is the probability that Los Angeles Dodgers wins the division? [5 pts](d) What is the probability to have an additional playoff game? [5 pts]2Maximum LikelihoodSuppose we have n i.i.d (independent and identically distributed) data samples from the following probabilitydistribution. This problem asks you to build a log-likelihood function, and find the maximum likelihoodestimator of the parameter(s).1 

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