The number of claims in a year follows a Poisson distribution with mean20. When there is a claim, the amount of (random) payment follows a zero-truncatedPoisson distribution with parameter )and of the Poisson distribution. Calculate the probability that there are no payments of1 and 2 in the given period.2. The payments are independent of each other

Poisson distribution occurs in business situations in which there are a few successes against a…

Answered: The number of claims in a year follows…

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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The lowest portfolio risk will result when the asset returns are perfectly positively correlated. Select one: True False
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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
The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3 accidents per year. Find the probability that less than three months elapse between accidents.
It is known from past experience that in a certain plant there are on the average 4 incidents per month. Find the proba- bility that in a given year there will be less than 4 accidents. Assume Poisson distribution.
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random. Assume that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4 customer per minute can be used to describe the arrival pattern. Assume further that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute a.Use the single-channel drive-up bank teller operation to determine the average arrival time in minutes of customers b.Use the single-channel drive-up bank teller operation to determine the average service time in minutes of the drive-up teller.
The number of orders arriving at an online vendor over the course of a day has a Poisson distribution with expectation 1200. All of the orders are independent, and each order has a cost represented by ?? . The expectation of this cost is 60 ?? and the variance is 120 ??2 . Calculate the expectation and the variance of the daily money flowing into this online vendor as a result of these orders.
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(b) Suppose the number of customers at a Sushi outlet is Poisson distributed where an average of nineteen customers are served per 30 minutes. (i) Over a fifteen-minute period, how many customers are served on average? Find the probability of exactly seven customers served over a fifteen-minute period. Write your answer correct to 4 decimal places. (iii) Calculate the probability at least 1 customer is served over a fifteen-minute period. Write your answer correct to 4 decimal places.
The Johnson & Johnson Company operates 6 identical machines that are serviced by a single technician when they breakdown. These breakdowns occur according to the Poisson distribution and average 0.03 breakdowns per machine operating hour. Average repair time for a machine is 5 hours and follows the exponential distribution. a) What percent of the technician's time is spent repairing machines? Answer in 4 decimal places. Blank 1 b) On average, how long is a machine out of service because of a breakdown? Answer in 2 decimal places. Blank 2 c) On average, how many machines are out of service? Answer in 1 decimal place. Blank 3 Blank 1 Blank 2 Blank 3 Add your answer Add your answer Add your answer

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