5. Let T be the time until a radioactive particle decays, and suppose (as is often done in physics and chemistry) that T ~ Expo() (a) The half-life of the particle is the time at which there is a 50% chance that the particle has decayed. Find the half-life of the particle. (b) Now consider n radioactive particles, with i.i.d. times until decay Ti, .. , In Expo(A). Let L be the first time at which one of the particles decays. Find the CDF of L. Also, find E(L) and Var(L) (c) Continuing (b), find the mean and variance of M = max(1, T,), the last time at which one of the particles decays. 5. Let T be the time until a radioactive particle decays, and suppose (as is often done in physics and chemistry) that T ~ Expo() (a) The half-life of the particle is the time at which there is a 50% chance that the particle has decayed. Find the half-life of the particle. (b) Now consider n radioactive particles, with i.i.d. times until decay Ti, .. , In Expo(A). Let L be the first time at which one of the particles decays. Find the CDF of L. Also, find E(L) and Var(L) (c) Continuing (b), find the mean and variance of M = max(1, T,), the last time at which one of the particles decays