RMI 2101 Spring 2016 Homework Assignment 5 24 Points Due on Monday, February 22, 2016 AT THE BEGINNING OF CLASS Be careful to follow the Guidelines for Homework Document located in the Course Documents Section of Blackboard. You will lose points for not following proper format. This homework assignment has to be typed and submitted to Safe Assign. 1. The Temple basketball team is playing the Villanova University (ranked No.1) on Wednesday February 17, 2016. Suppose that Temple has a 26.9% chance of winning the game. College basketball games cannot end in a tie. a. What is the random variable associated with this game? [1 point] b. What is the mutually exclusive event in this case? [1 point] c. Construct a well-labeled probability distribution table based on the outcomes of this game. [2 points] 2. 3. After Villanova University, Temple will play Date GAME February 17 February 21 February 23 February 27 March 3 March 6 Villanova Houston Tulsa UCF Memphis Tulane Win Probability1 26.9% 64.0% 46.1% 86.0% 55.0% 92.1% a. What is the probability that Temple wins ALL remaining games in the regular season (all the ones listed in the above table)? [2 points] b. Consider only the games in February. What is the probability that Temple loses ONLY ONE of the February games? Be sure to show your work. (Hint: they could lose against Villanova AND win the others OR they could lose against Houston AND win the others...) [4 points] Refer to Topic 4 article \"How Long a Shot Is Powerball\". In Figure 1, the probabilities for each combination of While Balls and Powerball are listed. Is the probability for each result (each White Balls/Powerball combination) an a priori probability or a statistical probability? Justify your answer. [2 points] 4. On Thursday, Amazon-Fresh is going to deliver a box of groceries to Restaurant A [Delivery A]. According to their contract, the promised time for delivery is 5:00AM. If the delivery arrives late, Amazon-Fresh will pay $15 penalty to Restaurant A. Based on past experience with the delivery, Amazon-Fresh estimates that this delivery has a 10% of chance of arriving late. Derive the probability distribution for total dollar losses. Note that is total dollar losses, not number of losses. Make sure that you label your table correctly. [2 points] 1 These win probabilities are randomly assigned. 5. On Friday, Amazon-Fresh is going to deliver another box of groceries to Restaurant B [Delivery B]. According to their contract, the promised time for delivery is 6:00AM. If the delivery arrives late, Amazon-Fresh will pay $20 penalty to Restaurant B. Based on past experience with the delivery, Amazon estimates that this delivery has a 20% of chance of arriving late. a. What are the possible outcomes for Amazon's total dollar amount of losses for delivery A and B? For each dollar amount of loss, describe under what circumstances it would occur. In other words, what has to happen in order for each dollar amount of losses to occur? Please note that this asks about total dollar amount of losses, not number of losses. [4 points] b. For each of the possible outcomes you identify in part [a], derive the probability of the outcome occurring. [4 points] c. Construct [in table form] the probability distribution for total dollar amount of losses for delivery A and B. [2 points]