During the night shift in an A&E department (10 pm to 6am) patients arrived at department requiring emergency treatment. The arrival of emergencies may be modeled as a non-homogeneous Poisson process with hourly rate λ(t) = 2t/(1+t2), 0 ≤ t ≤ 8 Find the probability that at least one emergency is admitted between midnight and 2am. Enter your answer in three decinal points. Please provide answer to three decimal places