Problem 8.5. In the compound model for aggregate claims, let the frequency random variable N be negative binomial with parameters r = 15 and 3 = 5. Moreover, let the common distribution of the i.i.d. severity random variables {X;;j = 1,2,...} be the two-parameter Pareto with a = 3 and 0 = 10. Let our usual assumptions hold, i.e., let N be independent of {X;; j = 1,2,...}. The insurer is interested in finding the total premium such that the aggregate losses exceed it with the probability less than or equal to 5%. Using the normal approximation, find such that P[S> ] = 0.05.
Problem 8.5. In the compound model for aggregate claims, let the frequency random variable N be negative binomial with parameters r = 15 and 3 = 5. Moreover, let the common distribution of the i.i.d. severity random variables {X;;j = 1,2,...} be the two-parameter Pareto with a = 3 and 0 = 10. Let our usual assumptions hold, i.e., let N be independent of {X;; j = 1,2,...}. The insurer is interested in finding the total premium such that the aggregate losses exceed it with the probability less than or equal to 5%. Using the normal approximation, find such that P[S> ] = 0.05.
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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![Problem 8.5.
In the compound model for aggregate claims, let the frequency
random variable N be negative binomial with parameters r = 15 and 3 = 5.
Moreover, let the common distribution of the i.i.d. severity random variables {X;;j =
1,2,...} be the two-parameter Pareto with a = 3 and 0 = 10.
Let our usual assumptions hold, i.e., let N be independent of {X;; j = 1,2,...}. The insurer
is interested in finding the total premium such that the aggregate losses exceed it with the
probability less than or equal to 5%. Using the normal approximation, find such that
P[S>T] = 0.05.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde697cfd-59ff-418e-8a17-3a00b6347cd3%2F3851caf8-143a-4620-b0b4-2435581e1f7b%2F2x8uti6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 8.5.
In the compound model for aggregate claims, let the frequency
random variable N be negative binomial with parameters r = 15 and 3 = 5.
Moreover, let the common distribution of the i.i.d. severity random variables {X;;j =
1,2,...} be the two-parameter Pareto with a = 3 and 0 = 10.
Let our usual assumptions hold, i.e., let N be independent of {X;; j = 1,2,...}. The insurer
is interested in finding the total premium such that the aggregate losses exceed it with the
probability less than or equal to 5%. Using the normal approximation, find such that
P[S>T] = 0.05.
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