Question: Let T be the time until a radioactive particle decays, and suppose (as is often done in physics and chemistry) that T Expo(λ).

(a) The half-life of the particle is the time at which there is a 50% chance that the particle has decayed (in statistical terminology, this is the median of the distribution of T). Find the half-life of the particle.

(b) Show that for ? a small, positive constant, the probability that the particle decays in the time interval [t, t + ?], given that it has survived until time t, does not depend on t and is approximately proportional to ?.