An insurance company has a portfolio of car insurance. For a given period of time, it is assumed that the drivers are classified in two categories: 'good drivers' and 'bad drivers'. The proportion of good drivers is 75% of the total drivers. We also know that the number of claims for a each driver is following Poisson with parameter A where A =1 for good drivers and A = 3 for bad drivers.

An insurance company has a portfolio of car insurance. For a given period of time, it is assumed that the drivers are classified in two categories: 'good drivers' and 'bad drivers'. The proportion of good drivers is 75% of the total drivers. We also know that the number of claims for a each driver is following Poisson with parameter A where A =1 for good drivers and A = 3 for bad drivers.

Name: An insurance company has a portfolio of car insurance. For a given pe
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: An insurance company has a portfolio of car insurance. For a given period of time, it is assumed thatthe drivers are classified in two categories: 'good drivers' and 'bad drivers'. The proportion of gooddrivers is 75% of the total drivers. We also k

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

See similar textbooks

Similar questions

A producer of pocket calculators purchases the main processor chips in lots of1,000. The producer would like to have a 1 percent rate of defectives but willnormally not refuse a lot unless it has 4 percent or more defectives. Samples of50 are drawn from each lot, and the lot is rejected if more than two defectives arefound.b. Compute A and B Use the Poisson approximation for your calculations
Suppose the customers arrive at a Poisson rate of on eper every 12 minutes, and that the service time is exponential at a rate of one service per 8 minutes. What are the average number of customers in the system(L) and the average time a customer spends in the system(W)?
The average demand on a factory store for a certain electric motor is 8 per week. When the storeman places an order for these motors, delivery takes one week. If the demand for motors has a Poisson distribution, how low can the storeman allow his stock to fall before ordering a new supply if he wants to be at least 95% sure of meeting all requirements while waiting for his new supply to arrive?
The manager of a market can hire either Mary or Alice. Mary, who gives you service at an exponential rate 20 customers per hour, can be hired at a rate of $3 per hour. Alice, who gives service at an exponential rate of 30 customers per hour, can hired at a rate of $C per hour. The manager estimates that, on the average, each customer’s time is worth $1 per hour and should be accounted for in the model. Assume customers arrive at a Poisson rate of 10 per hour. a) What is the average cost per hour if Mary is hired? If Alice is hired? b) Find C if the average cost per hour is the same for Mary and Alice.
In a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the prIn a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the premium loading factor is 0.25.emium loading factor is 0.25.
At 15:00 it is the end of the school day, and it is assumed that the departure of the students from school can be modelled by a Poisson distribution. On average, 24 students leave the school every minute. (e) There are 200 days in a school year. Given that Y denotes the number of days in the year that at least 700 students leave before 15:30, find (ii) P(Y > 150).
The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of grass seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species. (a) Suppose the company plans to spray a random sample of 400 seeds and conduct a two-sided test of 0: 0.8Hpusing = 0.05. They determine that the power of this test against the alternative 0.75pis 0.69. Interpret the power of this test.(b) Describe two ways the company can increase the power of the test. What is a disadvantage of each of these ways? (c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate of (0.726, 0.809). Use this confidence interval to determine whether the test described in…
Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. a) State the appropriate null and alternate hypotheses. b) Find the P-value. c) Should a change be made?
Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 149 of them met the specification. In a sample of 270 resistors purchased from vendor B, 233 of them met the specification. Vendor A is the current supplier, but if the data demonstrate convincingly that a greater proportion of the resistors from vendor B meet the specification, a change will be made. P-value?
A panel of dentists is interested in testing two different toothpaste brands (A and B) to see if there is a relationship between the brand and whether or not the patient has a cavity at their next appointment. A representative sample of 60 patients is recruited to take part in the study. At their first appointment of the year, each subject is assigned to brush their teeth with one of the two brands for the next six months. At their follow-up appointment six months later, they were checked for cavities. What method of data collection was used? Select one: a.Experiment b.Observational Study
A panel of dentists is interested in testing two different toothpaste brands (A and B) to see if there is a relationship between the brand and whether or not the patient has a cavity at their next appointment. A representative sample of 60 patients is recruited to take part in the study. At their first appointment of the year, each subject is assigned to brush their teeth with one of the two brands for the next six months. At their follow-up appointment six months later, they were checked for cavities. To test for significance of their findings, which of the following should the dentists use? Select one: a.Paired t-test b.One-sample t-test for a mean c.Linear Regression d.One-sample Z-test for a proportion e.Chi-Square test for independence f.Two-Sample t-test g.One-sample Z-test for a mean
A panel of dentists is interested in testing two different toothpaste brands (A and B) to see if there is a relationship between the brand and whether or not the patient has a cavity at their next appointment. A representative sample of 60 patients is recruited to take part in this study. At their first appointment of the year, each subject is assigned to brush their teeth with one of the two brands for the next six months. At their follow-up appointment six months later, they were checked for cavities. ******In the sample, 6 of the 30 patients assigned to Brand A were found to have a cavity. The fraction 6/30 should be denoted by which of the following? μ x̄ p p̂ n s σ χ²