***Please round ALL VALUES to the nearest 2 decimal places 1. Jasper Glass is taking 2 classes at Temple this semester. He is taking Marketing and Swimming. He knows he will earn either an A or a B in each class. He has an 70% chance for an A in Marketing and a 35% chance for an A in Swimming. Remember from a point system an A is worth 4 points and a B is worth 3. What is Jasper's expected GPA this semester? (4 points) 2. Matt started his own company where he rents used textbooks to struggling college students at multiple Universities for a low rate. Over the last few years Matt has been able to collect a total of 250 textbooks for his business at Temple University. Unfortunately, students can be irresponsible and lose their textbook rental causing a loss for Matt. Based on past information Matt has collected the data below for Temple University based on losses per semester. # of losses per semester 0 10 15 20 25 Probability 0.08 0.16 0.28 0.32 0.14 0.02 a. b. Calculate the expected frequency of losses per semester. (2 points) Calculated the variance. (2 points) 3. Now assume that when losses do occur, they are non-random and losses equal $60. a. Calculate the expected losses per semester? (2 points) b. Calculate the expected losses for ALL textbooks per semester. (1 point) c. Calculate the expected losses for ALL textbooks for the next 2 school years (4 semesters). (1 point) 4. Matt rents his textbooks to both Temple and Drexel University. He has 200 textbooks available for rental for Drexel students. Based on past information, Matt has collected the data below on losses per semester at Drexel. Assume each student only rents one textbook from Matt. # of losses per semester 0 7 14 21 28 # of students having these losses 25 50 75 ??? 10 a. b. Calculate the probability distribution for frequency based on the information provided above. (2 points) Matt would like to know which University faces the most risk for textbook losses between Temple and Drexel? Show/explain how you came to this answer. (2 points) 5. From past information, Matt collected Drexel University's losses when losses do occur. $ amount of losses 15 35 50 80 Probability of dollar loss 0.11 0.30 0.55 0.04 a. Calculate the expected value of severity for Drexel. (1 point). b. Calculate the expected loss per semester. (1 point) 6. Chris is a high school baseball player looking to play in college. He is obsessed with keeping track of his stats to keep improving. He has collected the below data on number of hits per game for a whole season which consists of 25 games. # of Hits 0 1 2 3 4 # of Games 3 6 ??? 7 4 a. Create a probability distribution. (1 point) b. Calculate the coefficient of variation. (2 points) 7. Five students are enrolled in RMI 2101. Matt has a 3.75 GPA, Maya has a 3.3 GPA, Nicole has a 3.0 GPA, Holden has a 2.8 GPA, and Mary has a 2.0 GPA. Matt has a variance of 0.75, Maya has a variance of 0.50, Nicole has a variance of 1.2, Holden has a variance of 1, and Mary has a variance of 0.3. Who faces the most risk? You must show the calculation for each student. (4 points) 8. Vail, Colorado gets a lot of snow throughout the winter months. These snowstorms can cause damage to electrical wiring within the town. Below is the probability distribution for the possible losses associated with these snowstorms. Losses (S) 0 1000 2500 4000 Probability 0.06 0.44 0.37 0.13 a. What is the maximum possible loss? (1 point) b. What is the expected loss? (1 point) c. What is the variance? (1 point)