Question

In: Math

Assume that a driver faces the following loss distribution: Loss 10,000 0 Probability .04 .96 These...

Assume that a driver faces the following loss distribution:

Loss 10,000 0

Probability .04 .96

These two drivers decide to pool their losses with two other drivers with the same loss distribution, and all losses are not correlated, i.e., independent.

6. What is the expected loss for each member of the pool?
7. What is the standard deviation of loss for each member of the pool?

Now consider another group of four drivers who have formed a separate pool, and who each have this loss distribution( before pooling):

Loss
15,000 10,000 0

Probability

.01 .05 .94

8. What is the expected loss for each member of this new pool of four drivers (after pooling)?

9. What is the standard deviation of loss for each member of this new pool (after pooling)?

10. If all 8 drivers decide to pool their risks, what would the expected loss for each member of this pool of eight drivers be?

Solutions

Expert Solution


Related Solutions

Assume that the following probability distribution exists for automobile damages Possible Outcomes for Damages Probability $0...
Assume that the following probability distribution exists for automobile damages Possible Outcomes for Damages Probability $0 50% 600 30% 2,000 10% 7,000 6% 11,000 4% What is the expected value for damages? A. $12.40 B. $124 C. 1,240 D. 12,400 Can someone please explain how you got the answer. I'm stuck
3. Consider Brown Dog brewing company’s workers compensation loss distribution. Loss Probability $ 0 0.4 1,000...
3. Consider Brown Dog brewing company’s workers compensation loss distribution. Loss Probability $ 0 0.4 1,000 0.35 10,000 0.17 100,000 0.075 1,000,000 0.005 a. Calculate the expected loss and standard deviation of this loss distribution. In addition, produce a graph showing the discrete loss distribution (already shown in Excel as an example). b. Assume that Brown dog Co. pools their workers compensation exposure with another brewery with the same loss outcome and probability. Assume these two breweries’ losses are uncorrelated...
Suppose that every driver faces a 2% probability of an automobile accident every year.
4. Individual Problems 20-4Suppose that every driver faces a 2% probability of an automobile accident every year. An accident will, on average, cost each driver $13,000. Suppose there are two types of individuals: those with $78,000.00 in the bank and those with $3,250.00 in the bank. Assume that individuals with $3,250.00 in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. Assume that both types of individuals are...
Suppose that every driver faces a 4% probability of an automobile accident every year. An accident...
Suppose that every driver faces a 4% probability of an automobile accident every year. An accident will, on average, cost each driver $13,000. Suppose there are two types of individuals: those with $104,000.00 in the bank and those with $6,500.00 in the bank. Assume that individuals with $6,500.00 in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. Assume that both types of individuals are only slightly risk...
Suppose that every driver faces a 4% probability of an automobile accident every year. An accident...
Suppose that every driver faces a 4% probability of an automobile accident every year. An accident will, on average, cost each driver $7,000. Suppose there are two types of individuals: those with $56,000.00 in the bank and those with $3,500.00 in the bank. Assume that individuals with $3,500.00 in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. Assume that both types of individuals are only slightly risk...
Suppose every driver faces a 1% probability of an automobile accident every year. An accident will,...
Suppose every driver faces a 1% probability of an automobile accident every year. An accident will, on an average cost each driver $10,000. Suppose there are two types of individuals: those with $60,000 and those with $5,000 in the bank. Assume that individuals with $5,000 in the bank declare bankruptcy if they get in an accident. In the bankruptcy, creditors receive only what individuals have in the bank. What price are individuals with $5,000 in the bank willing to pay...
16 . Individual Problems 20-4 Suppose that every driver faces a 5% probability of an automobile...
16 . Individual Problems 20-4 Suppose that every driver faces a 5% probability of an automobile accident every year. An accident will, on average, cost each driver $14,000. Suppose there are two types of individuals: those with $84,000.00 in the bank and those with $3,500.00 in the bank. Assume that individuals with $3,500.00 in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. Assume that both types of...
Use the Central Limit Theorem to calculate the following probability. Assume that the distribution of the...
Use the Central Limit Theorem to calculate the following probability. Assume that the distribution of the population data is normally distributed. A person with “normal” blood pressure has a diastolic measurement of 75 mmHg, and a standard deviation of 4.5 mmHg. i) What is the probability that a person with “normal” blood pressure will get a diastolic result of over 80 mmHg, indicating the possibility of pre-hypertension? ii) If a patient takes their blood pressure every day for 10 days,...
Problem Set I 1) Rick’s Toy Store faces the following probability distribution of fire losses in...
Problem Set I 1) Rick’s Toy Store faces the following probability distribution of fire losses in its store over the next year: Probability 0.50 0.40 0.10 Loss $0 $20,000 $70,000 Calculate the expected value and standard deviation of Rick’s losses for the year. Assume that Rick pools his losses with Mark’s store, which has an identical loss distribution. Mark’s losses are independent of Rick’s. Rick and Mark agree to split the total losses in the pool equally. Show the revised...
4. Consider the triangular probability distribution with PDF f(x) = 0 if x <= 0 or...
4. Consider the triangular probability distribution with PDF f(x) = 0 if x <= 0 or x >= 4, x/2 if 0 < x <= 1, (4-x)/6 if 1 < x < 4. (a) Obtain the CDF F (b) Obtain its inverse F^-1 (c) Describe the inverse CDF simulation method for this given problem.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT