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...

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)?