Question

In: Statistics and Probability

You are given: (iv) The claim frequency for a single insured follows a Poisson distribution with...

You are given:
(iv) The claim frequency for a single insured follows a Poisson distribution with mean ?.
(v) The claim frequency rate, ?, has a gamma distribution with mean 1/10 and variance 4/10000
.
(vi) During the last 3 years, 150 claims have occurred.
(vii) In each of the three years, 200 policies were in force.
Determine the Bayesian estimate of the posterior claim frequency rate based upon the latest
observation

Solutions

Expert Solution

orchestra answered 2 years ago
Next > < Previous

Related Solutions

You are given: (iv) The claim frequency for a single insured follows a Poisson distribution with...
You are given: (iv) The claim frequency for a single insured follows a Poisson distribution with mean ?. (v) The claim frequency rate, ?, has a gamma distribution with mean 1/10 and variance 4/10000 . (vi) During the last 3 years, 150 claims have occurred. (vii) In each of the three years, 200 policies were in force. Determine the Bayesian estimate of the posterior claim frequency rate based upon the latest observation.
The number of views of a page on a Web site follows a Poisson distribution with...
The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute. (i) What is the probability of no views in a minute? (ii) What is the probability of two or fewer views in 10 minutes? (iii) What is the probability of two or fewer views in 2 hours?
Losses follow a Poisson frequency distribution with a mean of 2 per year. The amount of...
Losses follow a Poisson frequency distribution with a mean of 2 per year. The amount of a loss is 1,2, or 3 with each having a probability of 1/3. Loss amounts are independent of the number of losses and from each other. An insurance policy covers all losses in a year subject to an annual aggregate deductible of 2. Calculate the expected claim payments for this insurance policy.
In a Poisson process, the probability of a single occurrence of the event in a given...
In a Poisson process, the probability of a single occurrence of the event in a given interval is proportional to the dimension of the interval.
The number of airplane landings at a small airport follows a Poisson distribution with a mean...
The number of airplane landings at a small airport follows a Poisson distribution with a mean rate of 3 landings every hour. 4.1 (6%) Compute the probability that 3 airplanes arrive in a given hour? 4.2 (7%) What is the probability that 8 airplanes arrive in three hours? 4.3 (7%) What is the probability that more than 3 airplanes arrive in a period of two hours?
Suppose the number of earthquakes occurring in an area approximately follows a Poisson distribution with an...
Suppose the number of earthquakes occurring in an area approximately follows a Poisson distribution with an average rate of 2 earthquakes every year. a.) Find the probability that there will be 1 to 3 (inclusive) earthquakes during the next year in this area. b.) Find the probability that there will be exactly 5 earthquakes during the next 3 year period. c.) Consider 10 randomly selected years during last century. What is the probability that there will be at least 3...
The number of people arriving at an emergency room follows a Poisson distribution with a rate...
The number of people arriving at an emergency room follows a Poisson distribution with a rate of 9 people per hour. a) What is the probability that exactly 7 patients will arrive during the next hour? b. What is the probability that at least 7 patients will arrive during the next hour? c. How many people do you expect to arrive in the next two hours? d. One in four patients who come to the emergency room in hospital. Calculate...
The number of people crossing at a certain traffic light follows a Poisson distribution with a...
The number of people crossing at a certain traffic light follows a Poisson distribution with a mean of 6 people per hour. An investigator is planning to count the number of people crossing the light between 8pm and 10pm on a randomly selected 192 days. Let Y be the average of the numbers of people to be recorded by the investigator. What is the value of E[Y ]? A. 6 B. 12 C. 1152 D. 0.03125. What is the value...
If student arrivals to the school dining commons follows the Poisson distribution with a mean of...
If student arrivals to the school dining commons follows the Poisson distribution with a mean of 50 students per day. For a randomly selected 36 days: (use 4 digits after decimal point) What is the probability that they served breakfast to at least 1757 students during these 36 days? [hint: P(ΣX ≥ 1757 students) =?]
The number of people arriving at an emergency room follows a Poisson distribution with a rate...
The number of people arriving at an emergency room follows a Poisson distribution with a rate of 7 people per hour. a. What is the probability that exactly 5 patients will arrive during the next hour? (3pts) b. What is the probability that at least 5 patients will arrive during the next hour? (5pts) c. How many people do you expect to arrive in the next two hours? (4pts) d. One in four patients who come to the emergency room...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT