Let ({N(t), t geq 0}) be an inhomogeneous Poisson process with intensity function [lambda(t)=0.8+2 t, quad t

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Let \(\{N(t), t \geq 0\}\) be an inhomogeneous Poisson process with intensity function

\[\lambda(t)=0.8+2 t, \quad t \geq 0\]

Determine the probability that at least 500 Poisson events occur in \([20,30]\).

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