Suppose that Boston Red Sox and New York Yankees (two AmericanLeague baseball teams) are scheduled to play a best of threeseries. The winner of the series will be the first team that winstwo of the three games. The probability that the Red Sox win a gamein their home stadium is 0.6 and the probability that the Yankeeswin their home game is 0.57. Next, suppose that you place a bet oneach 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 of the games areindependent of each other.

•Part 1:If the first game is played in Boston, the second gameis played in New York, and the third game (if it becomes necessary)is in Boston, then complete parts (i)-(v) below.

(i) Calculate the probability that the Red Sox will win theseries.

(ii) Construct a probability distribution for your net win(X) inthe series. Calculate your expected net win (the mean of X) and thestandard deviation of X.

(iii) Use Excel (share screenshot) and create 10,000 randomvalues for X. Let these random values be denoted by Y. Use these Yvalues to estimate your expected net win by using a 95% confidenceinterval. Does this confidence interval contain E(X)?

(iv) Construct a frequency distribution for Y. Next, use theChi-squared goodness of fit test to verify how closely thedistribution of Y has estimated the distribution of X.

(v) Use your observations of parts (ii) and (iii) above todescribe whether your betting strategy is favorable to you. Write asummary of your observations and analyses in the Word document.

•Part 2:Repeat part 1 above but assume that the first game isplayed in New York, the second game is played in Boston, and thethird game (if it becomes necessary) is in New York.

•Part 3:Repeat part 1 above but now assume that the series is abest-of-five series where the first team that wins three games winsthe series with games alternating between Boston and New York, withthe first game being played in Boston