Question

Hello, my question is actually in regards to risk management insurance . Here is the questions I need assistance with.

3. On Monday, Spring Grocery is expecting to receive Package A containing $8,000 worth of food. Based on the past experience with the delivery service, the manager estimates that this package has a chance of 5% being lost in shipment. On Wednesday, Spring Grocery expects Package B to be delivered. Package B contains $6,000 worth of food. This package has a 4% chance of being lost in shipment. a. What are the possible outcomes for Spring Grocery's total dollar amount of losses for package A and B? For each dollar amount of losses, describe under what circumstances it would occur. In other words, what event(s) must happen for each dollar amount of losses to occur? Please note that this asks about total dollar amount of losses, not number of losses. [2 points] For each of the possible outcomes you identify in part [al, derive the probability of the outcome occurring. [4 points] b. Construct [in table form] the probability distribution for total dollar amount of losses for package A and B. [2 points] c. Calculate the expected value of total dollar amount of losses. What is the unit of measurement? [2 points] d. The manager has calculated the variance for the total dollar amount of losses to be 4,422,400. Since you want to be sure you are using correct numbers in your evaluation, prove that the manager calculated the correct variance for total dollar amount of losses. Show all work! What is the unit of measurement? [4 points] Temple volleyball team will have a match with LMU on August 24, 2019. Temple has a 65% chance of winning the game. College volleyball games cannot end in a Suppose that tie. 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] After LMU, Temple will play against three other teams as listed in the table below DateGAME Win Probability Aug 24 LMU 65% Aug 25 Hofstra 40% Aug 31 Penn State 25% 30% Sep1 Texas A&M What is the probability that Temple wins ALL four games? [1 point] b.What is the probability that Temple loses ONLY ONE of the four games? Be sure to show your work. (Hint: they could lose to LMU AND win the others, OR they could lose to Hofstra AND win the others ...) [5 points]

Answer 1

3. Sol:

There are a total of 4 possible cases:

Both A and B are lost, in which case total loss is $14000.

A is received but B is lost, in which case total loss is $6000.

B is received but A is lost, in which case total loss is $8000.

Both A and B are received, in which case total loss is $0.

Since delivery of A is independent of delivery of B, keeping this in mind the probability values are calculated as shown below:

Let L denote the total loss.

P(L=14000) = 0.05*0.25 = 0.0125

P(L=6060) = 0.95*0.25 = 0.2375

P(L=8000) = 0.05*0.96 = 0.048

P(L=0) = 0.95*0.96 = 0.912

The expected value of dollar amount loss is:
E(L) = 14000*0.05 + 8000*0.20 + 60000*0.15 + 0*0.60 = $3200

Var(L) = 14000²*0.05 + 8000²*0.20 + 6000²*0.15 + 0²*0.60 - (3200)² =17760000$²

Thus the variance has been correclty calculated. The units are dollar squared.