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Determine the optimal renewal interval t

Questions:

1. Determine the optimal renewal interval τ and the corresponding maintenance ∗ cost rate for policy 1 (section 3.2.6.2) given that the system lifetime has a K(τ) Weibull distribution with form parameter and scale parameter θ; β > 1, θ > 0

2. Clients arrive at an insurance company according to a mixed Poisson process the structure parameter L of which has a uniform distribution over the interval [0, 1].

(1) Determine the state probabilities of this process at time t.

(2) Determine trend and variance function of this process.

(3) For what values of α and β are trend and variance function of a Polya arrival process identical to the ones obtained under (2)?

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