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8. S1 and S2 are random variables representing total claim amounts in two portfolios, and both can be well modeled by compound Poisson distributions. S₁ = Y₁++YN₁ where N₁ is Poisson with parameter A₁ = 2 and the claim size random variable Y has a distribution given by Y = 200 prob = 0.5 300 prob = 0.3 400 prob 0.2. = Similarly, S₂ = Z₁ + ··· + Z№2 where №2 is Poisson with parameter A23 and the claim size random variable Y has a distribution given by = 300 prob = 0.1 Z = 400 prob = 0.3 500 prob=0.6. = If S1 and S2 are independent, what is the probability distribution of SS1S2? What are its mean, variance and moment generating function? What is P[S 400]? Use the recursive formula to find PS r] for r≤ 2000.

8. S1 and S2 are random variables representing total claim amounts in two portfolios, and both can be well modeled by compound Poisson distributions. S₁ = Y₁++YN₁ where N₁ is Poisson with parameter A₁ = 2 and the claim size random variable Y has a distribution given by Y = 200 prob = 0.5 300 prob = 0.3 400 prob 0.2. = Similarly, S₂ = Z₁ + ··· + Z№2 where №2 is Poisson with parameter A23 and the claim size random variable Y has a distribution given by = 300 prob = 0.1 Z = 400 prob = 0.3 500 prob=0.6. = If S1 and S2 are independent, what is the probability distribution of SS1S2? What are its mean, variance and moment generating function? What is P[S 400]? Use the recursive formula to find PS r] for r≤ 2000.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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8. S1 and S2 are random variables representing total claim amounts in two portfolios, and both can be well modeled by compound Poisson distributions. S₁ = Y₁++YN₁ where N₁ is Poisson with parameter A₁ = 2 and the claim size random variable Y has a distribution given by Y = 200 prob = 0.5 300 prob = 0.3 400 prob 0.2. = Similarly, S₂ = Z₁ + ··· + Z№2 where №2 is Poisson with parameter A23 and the claim size random variable Y has a distribution given by = 300 prob = 0.1 Z = 400 prob = 0.3 500 prob=0.6. = If S1 and S2 are independent, what is the probability distribution of SS1S2? What are its mean, variance and moment generating function? What is P[S 400]? Use the recursive formula to find PS r] for r≤ 2000.
Transcribed Image Text:8. S1 and S2 are random variables representing total claim amounts in two portfolios, and both can be well modeled by compound Poisson distributions. S₁ = Y₁++YN₁ where N₁ is Poisson with parameter A₁ = 2 and the claim size random variable Y has a distribution given by Y = 200 prob = 0.5 300 prob = 0.3 400 prob 0.2. = Similarly, S₂ = Z₁ + ··· + Z№2 where №2 is Poisson with parameter A23 and the claim size random variable Y has a distribution given by = 300 prob = 0.1 Z = 400 prob = 0.3 500 prob=0.6. = If S1 and S2 are independent, what is the probability distribution of SS1S2? What are its mean, variance and moment generating function? What is P[S 400]? Use the recursive formula to find PS r] for r≤ 2000.
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