2. Consider a block of radio-active metal with a \"half-life\" of 1 day. Roughlyr speaking, this means that after 1 dag.r the amount of radiation is half of what it was at the beginning of the day, after two days it is lfnlth. after three days lfth1 etc. Let N: be the number of particles that arrive at a Geiger counter during [mt] {hours}. {a} Is it reasonable to assume that [NI] is a Poisson process with time dependent rate Mt) rfd = c x e) r We put from now on c = 1i] [per hour}. t in hours)1 for some constant c [c is called the initial rate}? {h} How many particles arrive on the average during the rst two days? Also nd Var|:N4g). [:1] Calculate the probability that more than 3 particles arrive in the rst ten minutes of the rst day. Do the same for the rst ten minutes of the second day