One Entry Level Statistics Task
Problem:
Suppose that Boston Celtics and Miami Heat (two American NBA teams) are scheduled to play a best of three (3) series. The winner of the series will be the first team that wins two of the three games. The probability that Boston Celtics wins a game in their home stadium (@TD Garden) is 0.63 and the probability that Miami Heat wins their home game (@Miami-Dade Arena) is 0.61. Next, suppose that you place a bet on each game played where you win $100 if Boston Celtics win and you lose $103 if Boston Celtics lose the game.
In parts 1-4 below, assume that the outcomes of the games are independent of each other.
Part 1:
If the first game is played in Miami, the second game is played in Boston, and the third game (if it becomes necessary) is in Miami, then complete parts (i)-(v) below.
(i) Calculate the probability that Boston Celtics will win the series.
(ii) Construct a probability distribution for your net win (X) in the series. Calculate your expected net win (E(X)) and the standard deviation of X.
(iii) Use Excel or R to create 2,500 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 90% confidence interval. Does this confidence interval contain the E(X) in (ii)?
(iv) Construct a frequency distribution for Y. Next, use the Chi-square goodness of fit test to verify how closely the distribution of Y has estimated the distribution of X.
(v) Use your observations in 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.
Part 2:
Repeat part 1 above but assume that the first game is played in Boston, the second game is played in Miami, and the third game (if it becomes necessary) is in Boston.
Part 3:
Repeat part 1 above but now assume that the series is a best of five (5) series where the first team that win three games will win the series with games alternating between Boston and Miami, with the first game being played in Miami.
Part 4:
Repeat part 1 above but now assume both teams will play in the 2025 NBA Finals. The series is a best of seven (7) series where the first team that win four games will win the series. The team with home-court advantage hosts games 2, 3, 5, and 6, while the opponent hosts games 1, 4, and 7. Let’s assume Boston Celtics has the home-court advantage against Miami Heat.
Hint: You can use R or Python(Jupyter Notebook) to solve Part 4.
