A flow of claims arriving at an insurance company is represented by a homogeneous Poisson process Nt in continuous time. (For now, we just count the number of claims arrived by time t.) Suppose that the mean inter-arrival time is equal to 1/λ, where > is a positive parameter. Let the unit of time be an hour. Question 8 What is E{N₁} ? (In N₁ the sub index 1 is a time (one hour).) X 1²

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A flow of claims arriving at an insurance company is represented by a homogeneous Poisson process Nt in continuous time. (For
now, we just count the number of claims arrived by time t.) Suppose that the mean inter-arrival time is equal to 1/λ, where A is a
positive parameter. Let the unit of time be an hour.
Question 8
What is E{N₁} ? (In N₁ the sub index 1 is a time (one hour).)
1
1²
1
1
Question 9
Are the r.v.'s N₁ and N₂ independent? (The sub index 2 in N₂ is a time (two hours).)
Yes
No
Question 10
Are the r.v.'s N₁ and N₂ – N₁ dependent?
Yes
No
Transcribed Image Text:A flow of claims arriving at an insurance company is represented by a homogeneous Poisson process Nt in continuous time. (For now, we just count the number of claims arrived by time t.) Suppose that the mean inter-arrival time is equal to 1/λ, where A is a positive parameter. Let the unit of time be an hour. Question 8 What is E{N₁} ? (In N₁ the sub index 1 is a time (one hour).) 1 1² 1 1 Question 9 Are the r.v.'s N₁ and N₂ independent? (The sub index 2 in N₂ is a time (two hours).) Yes No Question 10 Are the r.v.'s N₁ and N₂ – N₁ dependent? Yes No
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