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. Q14 Let K₁, K2, K3 be the r.v.'s presenting the numbers of claims whose size are equal respectively to 10, 20, and 30 (That is, K₁ is the number of claims whose sizes are equal exactly to 10, K₂ is the number of claims whose sizes are equal exactly to 20. and K₂ is the number of claims whose sizes
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. Q14 Let K₁, K2, K3 be the r.v.'s presenting the numbers of claims whose size are equal respectively to 10, 20, and 30 (That is, K₁ is the number of claims whose sizes are equal exactly to 10, K₂ is the number of claims whose sizes are equal exactly to 20. and K₂ is the number of claims whose sizes
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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.
Q14
Let K₁, K2, K3 be the r.v.'s presenting the numbers of claims whose size are equal respectively to
10, 20, and 30 (That is, K₁ is the number of claims whose sizes are equal exactly to 10, K₂ is the
number of claims whose sizes are equal exactly to 20, and K3 is the number of claims whose sizes
are 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 No
O Depends on a situation.
Yes](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb924e824-f7b8-486a-bee8-48b1feb67b77%2F45a6ae8c-338b-4f4a-9e70-9716021776fc%2Fovbyy22_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.
Q14
Let K₁, K2, K3 be the r.v.'s presenting the numbers of claims whose size are equal respectively to
10, 20, and 30 (That is, K₁ is the number of claims whose sizes are equal exactly to 10, K₂ is the
number of claims whose sizes are equal exactly to 20, and K3 is the number of claims whose sizes
are 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 No
O Depends on a situation.
Yes
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