OK, if I understand correctly - the waiting time between events is an Exp(0.3) so the waiting time before the 2nd claim is Gamma(2,0.3). We could calculate probabilities by converting it to a chi-square distribution using: If \(X \sim ga(\alpha, \lambda)\) then \(2\lambda X \sim \chi ^2_{2\alpha}\) We can then use the chi-square probability tables.
