r an insurance portfolio that consists of two homogeneous groups of clients. Let N₂, (i=1.2) umber of claims occurred in the ith group. Suppose that N₁ and N₂ are independent and ow a Poisson distribution. Assume E {N₁} = 300 and E {N₂} = 700. of each individual claim from the first group is 10 (units of money) with probability 0.6, and s of money) with probability 0.4, The size of each individual claim from the second group is s of money) with probability 0.3, and 30 (units of money) with probability 0.7. e the total number of claims, and let S be the total aggregate claim. the questions 9-17. be the size of the ith claim arriving (whichever group it comes from). What's the distribution quals 10, 20 and 30 with probabilities 0.3, 0.35 and 0.35 respectively.
r an insurance portfolio that consists of two homogeneous groups of clients. Let N₂, (i=1.2) umber of claims occurred in the ith group. Suppose that N₁ and N₂ are independent and ow a Poisson distribution. Assume E {N₁} = 300 and E {N₂} = 700. of each individual claim from the first group is 10 (units of money) with probability 0.6, and s of money) with probability 0.4, The size of each individual claim from the second group is s of money) with probability 0.3, and 30 (units of money) with probability 0.7. e the total number of claims, and let S be the total aggregate claim. the questions 9-17. be the size of the ith claim arriving (whichever group it comes from). What's the distribution quals 10, 20 and 30 with probabilities 0.3, 0.35 and 0.35 respectively.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![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 and
both 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, and
20 (units of money) with probability 0.4, The size of each individual claim from the second group is
20 (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.
Q11
Let Y₂ be the size of the ith claim arriving (whichever group it comes from). What's the distribution
of Y₂?
OY; equals 10, 20 and 30 with probabilities 0.3, 0.35 and 0.35 respectively.
O Y₂ equals 10, 20, and 30 with probabilities 0.18, 0.33, and 0.49 respectively.
O Y₂ is uniform on {10,30].
O Y has Poisson distribution with parameter 1000.
O Y₂ has multinomial distribution with parameter (1000; 3/8, 5/8).
O Y has Poisson distribution with parameter 80.
Q12
Is it true that S' is a compound Poisson r.v. and can be written as S = N₁Y₁?
i=1
True
False](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb924e824-f7b8-486a-bee8-48b1feb67b77%2F8ca52bcf-b2ca-4fff-bf29-f7b97d618128%2F5tzvhd_processed.png&w=3840&q=75)
Transcribed Image Text: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 and
both 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, and
20 (units of money) with probability 0.4, The size of each individual claim from the second group is
20 (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.
Q11
Let Y₂ be the size of the ith claim arriving (whichever group it comes from). What's the distribution
of Y₂?
OY; equals 10, 20 and 30 with probabilities 0.3, 0.35 and 0.35 respectively.
O Y₂ equals 10, 20, and 30 with probabilities 0.18, 0.33, and 0.49 respectively.
O Y₂ is uniform on {10,30].
O Y has Poisson distribution with parameter 1000.
O Y₂ has multinomial distribution with parameter (1000; 3/8, 5/8).
O Y has Poisson distribution with parameter 80.
Q12
Is it true that S' is a compound Poisson r.v. and can be written as S = N₁Y₁?
i=1
True
False
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