A policyholder has a two-year auto insurance for his new car. Let X be the number of accidents th...
A policyholder has a two-year auto insurance for his new car.
Let X be the number of accidents that the policyholder experiences in one year.
You are given:
- Pr[X = 0] = 0.9
- Pr[X = 1] = 0.08
- Pr[X = 2] = 0.02
The number of accidents that the policyholder experiences in each year is independent.
Given that the policyholder experiences exactly 2 accidents in two years, find the probability that the policyholder experiences at least one accident in each of the two years.
Homework Answers
Given that the total number of accidents in 2 years is 2. This can happen in three ways: 0 accident in 1st year and 2 accidents in 2nd year, 2 accidents in 1st year and 0 accidents in second year, 1 accident in each year.
Hence,
P(Atleast one accident in each year | Total 2 accidents)
= P(1 Accident in each year | Total 2 accidents)
= 8/53
= 0.1509
Add Answer to:
A policyholder has a two-year auto insurance for his new car. Let X be the number of accidents th...
An insurance company has issued 100 policies. The number of claims filed under each policy follows a Poisson distribution with a mean 2. Assuming that the claims filed by each policyholder are in...
An insurance company has issued 100 policies. The number of claims filed under each policy follows a Poisson distribution with a mean 2. Assuming that the claims filed by each policyholder are independent of each other, what is the approximate probability that more than 220 claims will be filed by the group of policyholders? B) 0.159 A) 0.079 C) 0.444 D) 0.556 E) 0.921 Question 2-20 An actuary is studying claim patterns in an insurer's book of business. He compiles...
This year, the number of accidents, X, at an amusement park has probability generating function PX (t) = e−0.2(1−t) ,...
This year, the number of accidents, X, at an amusement park has probability generating function PX (t) = e−0.2(1−t) , where defined. The amusement park owner’s insurance company reimburses up to a maximum of one accident this year. Let Y be the number of unreimbursed accidents. Determine the probability generating function, PY (t) , of the number of unreimbursed accidents at this amusement park this year, where defined.
This year, the number of accidents, X, at an amusement park has probability generating function PX (t) = e−0.2(1−t) ,...
This year, the number of accidents, X, at an amusement park has probability generating function PX (t) = e−0.2(1−t) , where defined.The amusement park owner’s insurance company reimburses up to a maximum of one accident this year. Let Y be the number of unreimbursed accidents.Determine the probability generating function, PY (t) , of the number of unreimbursed accidents at this amusement park this year, where defined.
2. An insurance company estimates that for each individual, the probability of a car accident occurring...
2. An insurance company estimates that for each individual, the probability of a car accident occurring in a given year is 0.02. If an accident occurs, the amount of damage to the car is uniformly distributed on [2000, 4000]. What is the average loss that an insured experiences in a year? What is the variance?
7) Based on past records, the average number of two-car accidents in a New York City...
7) Based on past records, the average number of two-car accidents in a New York City police precinct is 10.1 per day. What is the probability that there will be: a) at least fourteen such accidents on any given day? b) not more than seven such accidents on any given day? c) at least seven but not more than twelve such accidents on any given day? d) fewer than ten such accidents on any given day?
The number of accidents per week at a busy intersection was recorded for a year. There...
The number of accidents per week at a busy intersection was recorded for a year. There were 19 weeks with no accidents, 17 weeks with one accident, 9 weeks with two accidents, and 7 weeks with three accidents. A week is to be selected at random and the number of accidents noted. Let X be the outcome. Then X is a random variable taking on the values 0, 1, 2, and 3. (a) Write out a probability table for X...
2) [2096] Penguin auto insurance estimates that there exists a .23 probability that 16-year-old d...
2) [2096] Penguin auto insurance estimates that there exists a .23 probability that 16-year-old driving a red, two-door, 8-cylinder engine car will get into an accident that would cost the maximum amount in liability of $100,000. The annual premium for such a policy is $2,500. Q1) What is the expected profit per year for Penguin on such a policy? Q2) What profit must Penguin charge in order to make a profit on each policy? 3.120%) Recent research at Viking auto...
Romeo and Juliet decide to start a new business venture: JR Insurance Ltd. to insure people...
Romeo and Juliet decide to start a new business venture: JR Insurance Ltd. to insure people against damages from car accidents. They assume that car accidents resulting in claims occur according to a nonhomogeneous Poisson process at rate ? ? = 2? per month. As almost any other insurance policy; there is a stochastic delay between the time each accident occurs and the payment is made. These claims not yet paid are said to be “outstanding claims.” Suppose that these...
1. (a) Consider the random variable Y having possible values 1, 2 and 3. The corresponding...
1. (a) Consider the random variable Y having possible values 1, 2 and 3. The corresponding probability for each value is: 1 with probability Y = 2 with probability 3 with probability Determine an expression for the probability mass function (pmf) (11) Determine the mean and the standard deviation of Y. (b) The probability that a man hits a target is and that of his son and daughter are and respectively. If they all fire together, find the probability that:...
An insurer has a portfolio of 1000 one-year term life insurance policies just issued to 1000...
An insurer has a portfolio of 1000 one-year term life insurance policies just issued to 1000 different (independent) individuals. Each policy will pay $1000 in the event that the policy holder dies within the year. For 500 of the policies, the probability of death is 0.01 per policyholder, and for the other 500 policies the probability of death is 0.02 per policyholder. Find the expected value and the standard deviation of the aggregate claim that the insurer will pay.
An insurance company has issued 100 policies. The number of claims filed under each policy follows a Poisson distribution with a mean 2. Assuming that the claims filed by each policyholder are independent of each other, what is the approximate probability that more than 220 claims will be filed by the group of policyholders? B) 0.159 A) 0.079 C) 0.444 D) 0.556 E) 0.921 Question 2-20 An actuary is studying claim patterns in an insurer's book of business. He compiles...
The number of accidents per week at a busy intersection was recorded for a year. There were 19 weeks with no accidents, 17 weeks with one accident, 9 weeks with two accidents, and 7 weeks with three accidents. A week is to be selected at random and the number of accidents noted. Let X be the outcome. Then X is a random variable taking on the values 0, 1, 2, and 3. (a) Write out a probability table for X...
2) [2096] Penguin auto insurance estimates that there exists a .23 probability that 16-year-old driving a red, two-door, 8-cylinder engine car will get into an accident that would cost the maximum amount in liability of $100,000. The annual premium for such a policy is $2,500. Q1) What is the expected profit per year for Penguin on such a policy? Q2) What profit must Penguin charge in order to make a profit on each policy? 3.120%) Recent research at Viking auto...
1. (a) Consider the random variable Y having possible values 1, 2 and 3. The corresponding probability for each value is: 1 with probability Y = 2 with probability 3 with probability Determine an expression for the probability mass function (pmf) (11) Determine the mean and the standard deviation of Y. (b) The probability that a man hits a target is and that of his son and daughter are and respectively. If they all fire together, find the probability that:...
Most questions answered within 3 hours.
-
In C++ Programming, Try using loops only.
This lab demonstrates the use of the While Loop...
asked 11 minutes ago -
Effect of DCMU and sodium azide on Chlamydomonas? We did an
experiment where we had Chlamydomonas...
asked 51 minutes ago -
1a) According to the ideal gas law, _______________.
a. a gas has infinite volume at absolute...
asked 2 hours ago -
Oakdale Fashions, Inc. had $245,000 in 2018 taxable income.
Using the tax schedule in Table 2.3...
asked 2 hours ago -
The marketing class at CSUS had an average score of 150. An
educational analyst determined that...
asked 4 hours ago -
Justin Case has purchased a $250 000 home by putting 20 % down
and taking out...
asked 4 hours ago -
1. In a labor market, marginal cost for a firm is
____________.
a. recruiting cost
b....
asked 4 hours ago -
On January 1, 2019, ABC Company issued $60,000,000 of 20-year,
10.5% bonds when the market rate...
asked 5 hours ago -
39.4% of US homes continue to use a landline in addition to cell
phone service. 3...
asked 5 hours ago -
Starting with benzene, synthesize 1-phenyl-1-butyne.
Show intermediates and reagents.
asked 6 hours ago -
Create a 32-run crossed array design with six control factors
and two noise factors such that...
asked 7 hours ago -
A 500g sample of sand from source A has the following amounts
retained on each sieve....
asked 7 hours ago