Mathematics — Probability · continuous-density-functions
Problem
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])=∫0Tλe−λtdt. 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.