Suppose you are watching a radioactive source that emits particles at a rate described by the exponential density f(t) = λe−λt , where λ = 1, so that the probability P(0, T) that a particle will appear in the next T seconds is P([0, T]) = R T 0 λe−λt dt. Find the probability that a particle (not necessarily the first) will appear
(a) within the next second.
(b) within the next 3 seconds.
(c) between 3 and 4 seconds from now.
(d) after 4 seconds from now
