Suppose you are testing a new software, and a bug causes errors randomly at a constant rate of three times per hour. What is the probability that the first bug will occur within the first ten minutes? ${}$
Let rate or intensity be λ = 3 per hour and t = 1/6 hours (10 minutes)
P(X < 1/6) = ${{\int}}_{0}^{\frac{1}{6}}{\mathrm{\lambda}}^{}{e}^{-\mathrm{\λt}}{DifferentialD;}t$ = 0.393
Therefore the probability that the first bug will occur in the next 10 minutes is 0.393.