Consider an insurance portfolio that consists of two homogeneous groups of clients. Let N₂, (i=1.2)be the number of claims occurred in the ith group. Suppose that N₁ and N₂ are independent andboth follow a Poisson distribution. Assume E {N₁} 300 and E {N₂} = 700.The size of each individual claim from the first group is 10 (units of money) with probability 0.6, and20 (units of money) with probability 0.4, The size of each individual claim from the second group is20 (units of money) with probability 0.3, and 30 (units of money) with probability 0.7.Let N be the total number of claims, and let S be the total aggregate claim.Answer the questions 9-17.Q14Let K₁, K2, K3 be the r.v.'s presenting the numbers of claims whose size are equal respectively to10, 20, and 30 (That is, K₁ is the number of claims whose sizes are equal exactly to 10, K₂ is thenumber of claims whose sizes are equal exactly to 20, and K3 is the number of claims whose sizesare equal exactly to 30.) Which distributions do K₁, K2, K3 have?O Poisson distributions with parameters 180, 330, and 490 respectively.O Poisson distributions with parameters 1000, 1000, 1000 respectively.O Exponential distribution with a parameters 300, 350, and 350 respectively.O Poisson distributions with parameters 300, 350, and 350 respectively.O Poisson distributions with parameters 1000/6, 1000/3, and 500 respectively.Q15=Let K₁, K2, K3 be r.v.'s defined in Question 14. Are K₁, K2, K3 dependent?O NoO Depends on a situation.Yes

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Answered: Consider an insurance portfolio that…

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
The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20-39 who regularly skip eating breakfast is 0.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size n = 500 of young adults ages 20-39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, X, in Lance's sample who regularly skip breakfast is greater than 122. You may find table of critical values helpful. Express the result as a decimal precise to three places. P(X > 122)%3D eal limir thaor tnr the hinamialdietrikotian tn indtha neohabilin: tbot the numbar of individuale in Aanly tha nd tems of use contact us he p about us cyeers 6:56 PM 11/6/2020 a. 2) Cip prt sc insert 110 |
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The annual rainfall (in inches) in a certain region is normally distributed with µ = 40 and σ = 4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? Suppose the rainfall in each year is independent of the rainfall in other years and the distribution of rainfall in each year is the same as in the present year.
23. Find the cumulant generating function of gamma distribution and obtain various cumulants.
4. An insurance company sells an automobile policy with a deductible of one unit. Let X be the amount of the loss having pmf 0.9 f(x) = x = 0 x = 1,2,3,4,5,6 where c is a constant. a) Find c. b) Find the expected value of the amount the insurance company must pay.
3. Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete probability function: 6x f(x) = e-6, for x = 0,1,2, ... a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.
The maintenance department in a factory claims that the number of breakdowns of a particular machine follows a Poisson distribution with a mean of 2 breakdowns every 428 hours. Let x denote the time (in hours) between successive breakdowns. (a) Find λ and Ux. (Write the fraction in reduced form.) ux = f(x) = 214 (b) Write the formula for the exponential probability curve of x. P(x <4) ✔ Answer is complete and correct. 1 P(115
The graph of the discrete probability to the right represents the number of live births by a mother 42 to 46 years old who had a live birth in 2015. Complete parts (a) through (d) below. 0.30 0-279 0.25 0.238 0,20- U.168 0.15 15 0.097 0.10 0.05 004 0036 0.043 0.00- 1 2 3 8 Number of Liive Births (a) What is the probability that a randomly selected 42- to 46-year-old mother who had a live birth in 2015 has had her fourth live birth in that year? 0.112 (Type an integer or a decimal.) (b) What is the probability that a randomly selected 42- to 46-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year? 0.206 (Type an integer or a decimal.) (c) What is the probability that a randomly selected 42- to 46-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year? 0.101 (Type an integer or a decimal.) hp esc & 8
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