Question: Advanced Stochastic process: Poisson process 4. (3 marks) An insurance company has three claim adjusters in its branch office. People with claims against the company

Advanced Stochastic process: Poisson process

Advanced Stochastic process: Poisson process 4.

4. (3 marks) An insurance company has three claim adjusters in its branch office. People with claims against the company are found to arrive according to the Poisson process at an average rate of 20 per eight hours working day. The amount of time an adjuster spends with a claimant is an independent exponential RV with the mean (service) time of 40 min. (a) Show the stationary dist. of the system exists. (b) How many hours a week can an adjuster expect to spend with the claimants? (c) How much time, on the average, does a claimant spend in the branch office? 4. (3 marks) An insurance company has three claim adjusters in its branch office. People with claims against the company are found to arrive according to the Poisson process at an average rate of 20 per eight hours working day. The amount of time an adjuster spends with a claimant is an independent exponential RV with the mean (service) time of 40 min. (a) Show the stationary dist. of the system exists. (b) How many hours a week can an adjuster expect to spend with the claimants? (c) How much time, on the average, does a claimant spend in the branch office

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