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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/A, where > is a positive parameter. Let the unit of time be an hour. Question 19 Suppose now that the sizes of claims are independent, and the size of a particular claim equals either 2 or 5 units of money with probabilities 2/3 and 1/3, respectively. Denote by K₁1 and K₁2 the numbers of claims by time t, amounting to 2 or 5, respectively. That is, for example, Kt1 is the number of claims by time t that exactly equal to 2.) What is E(Kt₁) ? 2xt 3Xt 2λt 4Xt

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/A, where > is a positive parameter. Let the unit of time be an hour. Question 19 Suppose now that the sizes of claims are independent, and the size of a particular claim equals either 2 or 5 units of money with probabilities 2/3 and 1/3, respectively. Denote by K₁1 and K₁2 the numbers of claims by time t, amounting to 2 or 5, respectively. That is, for example, Kt1 is the number of claims by time t that exactly equal to 2.) What is E(Kt₁) ? 2xt 3Xt 2λt 4Xt

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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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/A, where A is a positive parameter. Let the unit of time be an hour. Question 19 Suppose now that the sizes of claims are independent, and the size of a particular claim equals either 2 or 5 units of money with probabilities 2/3 and 1/3, respectively. Denote by Kt1 and Kt2 the numbers of claims by time t, amounting to 2 or 5, respectively. That is, for example, K₁₁ is the number of claims by time t that exactly equal to 2.) What is E(K+1) ? 2λt 3 3Xt 2λt 4Xt 3 Question 20 What is E(K+2) ? Xt 3 5Xt 3 2λt 3 5Xt
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/A, where A is a positive parameter. Let the unit of time be an hour. Question 19 Suppose now that the sizes of claims are independent, and the size of a particular claim equals either 2 or 5 units of money with probabilities 2/3 and 1/3, respectively. Denote by Kt1 and Kt2 the numbers of claims by time t, amounting to 2 or 5, respectively. That is, for example, K₁₁ is the number of claims by time t that exactly equal to 2.) What is E(K+1) ? 2λt 3 3Xt 2λt 4Xt 3 Question 20 What is E(K+2) ? Xt 3 5Xt 3 2λt 3 5Xt
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