In 2003 Andy Pettitte pitched for the New York Yankees baseball team, a team that won the
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In 2003 Andy Pettitte pitched for the New York Yankees baseball team, a team that won the American League pennant and qualified for the World Series. In the postseason, the Yankees played a series of games with each of three teams: Minnesota, Boston, and Florida. In each series, Pettitte pitched the second game and won. A prominent sportswriter noticed this and wrote an article touting this notable streak of wins when pitching the second game of a series. Over the season, Pettitte had pitched in 29 games and won 21 of them. Is this a streak? Why might the sportswriter believe this is a streak? How could you profit from this perception? Model the sportswriter's beliefs supposing that the individual has two mental urns. One urn (average) has three balls, with two marked "win" and one marked "lose." Suppose the other urn (streak) also has three balls but all are marked "win." Suppose that the urns are never refreshed. What is the lowest probability of a streak that would lead the sportswriter to interpret this series of wins as a streak? Suppose instead that the urns are refreshed after every two games. Now what must the unconditional probability of a streak be before one would believe one was observing a streak?
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Given that Pettite won 21 of 29 games we may think of the probability of him winning a game as approximately 23 Given this probability it would not be ...View the full answer
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