Consider an insurance portfolio that consists of two homogeneous groups of clients. Let Nį, (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.
Consider an insurance portfolio that consists of two homogeneous groups of clients. Let Nį, (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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please just solve for the question 13
Transcribed Image Text:Q13
Find E {S} and Var {S}.
(Hint: Compute E {Y; } and E {Y²} proceeding from the result of Question 10 and use Propositions 1-
2 that we proved in class regarding E {S} and Var {S} in the case where N is a Poisson r.v.)
E{S} = 1,000,000 and Var {S} = 1, 001, 000, 000
E{S} = 23, 100 and Var {S} = 591, 000
E {S} = 20, 500 and Var {S} = 485,000
E {S} = 80,000 and Var {S} = 6, 480,000
![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.
Q10
What in the mean and variance of N?
O 300 and 300
1,000 and 1,000
O 700 and 700
O 23,100 and 23,100
Q11
Let Y; be the size of the ith claim arriving (whichever group it comes from). What's the distribution
of Y₂?
O Y₂ 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 Y; is uniform on {10,30].
O Y₂ has Poisson distribution with parameter 1000.
O Y has multinomial distribution with parameter (1000; 3/8, 5/8).
O Y₂ has Poisson distribution with parameter 80.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb924e824-f7b8-486a-bee8-48b1feb67b77%2F881ab84e-cbd3-42c0-9e27-b93b0dea4268%2Fg9twj1_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.
Q10
What in the mean and variance of N?
O 300 and 300
1,000 and 1,000
O 700 and 700
O 23,100 and 23,100
Q11
Let Y; be the size of the ith claim arriving (whichever group it comes from). What's the distribution
of Y₂?
O Y₂ 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 Y; is uniform on {10,30].
O Y₂ has Poisson distribution with parameter 1000.
O Y has multinomial distribution with parameter (1000; 3/8, 5/8).
O Y₂ has Poisson distribution with parameter 80.
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