An insurance company assumes that the number of claims in a year has a Poissondistribution of mean A and that this number is independent from year to year.Suppose that aAssume that an insured chosen randomly from a portfolio has the following numberof claims: 4, 0, 1, 2, 3, 0, 0, 1, 1, 0.a) Find a conjugate a priori density for A knowing that the company estimates asmore frequently 2 claims a year and that no more than 5 claims areacceptable in a year with a probability 0.97b) Determine a posteriori credibility interval at 99%.c) Obtain the marginal distribution of the number of claims and predict thenumber of claims in the following year using a 95% confidence interval.

In this problem, we are dealing with an insurance company's claim data and conducting a Bayesian…

Answered: An insurance company assumes that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider an auto insurance portfolio where the number of accidents follows a Poisson distribution with parameter λ= 1000. Suppose the damage sizes for separate accidents are i.i.d. (independent identically distributed) r.v.'s having an exponential distribution with a mean of $2500. Each policy involves a deductible of $500. Let N₁ be the number of accidents that result in claims, and N₂ be the number of accidents that do not result in claims. Answer the following questions 1-5. Q1 Are N₁, N₂ dependent? Q2 Depends on a situation, No Yes What is the name of the distributions of N₁, №₂? O Marked Poisson Gamma Exponential Compound Poisson
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Hello, For table 5 - t-distribution I am not sure how they are getting t when the d.f is more than 30 since the chart ends at 29. Thanks.
Suppose that the claim size distribution of an insurance portfolio follows a Pareto distribution of the form α+1 α f(x) β = B\B+x (i) Derive a formula for the rth moment, ar, of this Pareto distribution in terms of its (r-1) th moment, αr-1. Show your steps clearly with reasons. (ii) From this expression find α3 and α4 using the known result for the mean μ of the above Pareto distribution. (You may assume that α>r, where a is one of the two parameters of the Pareto distribution).
Q1) A document printing machine receives documents according to a Poisson process with an expected interarrival time of 5 minutes from the legal department. When the machine has just one document to print, the expected processing time is 5 minutes. When machine has more than one document, then it does not require initial set-up time and expected processing time for each document to 4 minutes. In both cases, the processing times have an exponential distribution. (a) Construct the rate diagram for this queueing system. (b) Check that this is a birth-and-death process and find the steady-state distribution of the number of documents in the system but not yet finished printing. (Hint: Use the sum of Geometric series) (c) Derive L and Lq for this system. (Hint: Use the sum of Arithmetic-Geometric series) (d) Use the information of L and Lq to determine W and Wq. Q2) Jacob runs a shoe repair store by himself. Customers arrive to bring a pair of shoes to be repaired according to a Poisson…
23. Find the cumulant generating function of gamma distribution and obtain various cumulants.
The times between arrivals in a queue follow an exponential distribution with a rate of 1. Check the incorrect alternative: a) 50% of arrivals will take place before 1 minute. b) If the times between arrivals are exponentially distributed with a rate equal to 1, then arrivals occur according to a Poisson distribution with an average equal to 1. c) Times between arrivals are independent. d) The variance of the times between arrivals is equal to 1. e) There is an average of one arrival every minute.
Suppose there are three possible states of nature, and the class-conditional PDFS are the Cauchy distributions 1 p(rw;) = 1 i = 1,2,3. (1) 2 1+ bị Let ai = -2, a2 = 0, az = 2, bị = b2 = 1, b3 = 0.5. Let P(wi) = P(w2) = 0.4, P(w3) = 0.2. (a) Find the decision boundaries and the decision regions for the Bayesian decision (b) Calculate the probability of error for the classification done according to this
In finance, one example of a derivative is a financial asset whose value is determined (derived) from a bundle of various assets, such as mortgages. Suppose a randomly selected mortgage in a certain bundle has a probability of 0.06 of default. (a) What is the probability that a randomly selected mortgage will not default? (b) What is the probability that four randomly selected mortgages will not default assuming the likelihood any one mortgage being paid off is independent of the others? Note: A derivative might be an investment that only pays when all four mortgages do not default. (c) What is the probability that the derivative from part (b) becomes worthless? That is, at least one of the mortgages defaults. (a) The probability is (Type an integer or a decimal. Do not round.)

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