Reference no: EM133370794

Suppose that Boston Red Sox and New York Yankees [two American League baseball teams) are scheduled to play a best of three series. The winner of the series will be the first team that wins two of the three games. The probability that the Red Sox win a game in their home stadium is 0.6 and the probability that Yankees win their home game is 0.57. Next, suppose that you place a bet on each game played where you win $500 if the Red Sox win and you lose $520 if the Red Sox lose the game. In parts 1-3 below, assume that the outcomes ofthe games are independent of each other.

Part 1: If the first game is played in Boston, the second game is played in New York, and the third game [if it becomes necessary} is in Boston, then complete parts [iJ-(vl below. (i) Calculate the probability that the Red Box will win the series. (ii) Construct a probability distribution for your net win (X) in the series. Calculate your expected net win (the mean of X) and the standard deviation of X.' {iii} Use Excel or R to create 10,000 random values for X. Let these random values be denoted by Y. Use these Y values to estimate your expected net win by using a 95% confidence interval. Does this confidence interval contain E(X)? {iv} Construct a frequency distribution for Y. Next, use the Chi-squared goodness of fit test to verify how closely the distribution of Y has estimated the distribution of X. (v) Use your observations of parts (ii} and (iii) above to describe whether your betting strategy is favorable to you. Write a summary of your observations and analyses in the Word document.