Please answer all parts of the following Statistics problem:

Suppose that we measure the decay of a quantity of Cesium 137, and our data indicates that the number of atoms that decay per minute can be modeled with a Poisson(4) random variable (in particular, the atoms decay at the rate of 4 per minute). Assuming our model is correct, the interdecay time (time between decay of atoms) can be modeled with an exponential random variable. (a) (7 points) Suppose T is the time we see the 5th atom decay. What kind of random variable is T, and what are its parameters? (b) (9 points) Suppose that we have not observed any atoms decay in the first 3 minutes. What is the probability that we will not see a decay until after minute 4 (i.c., there will be no decay event between 3 and 4 minutes of measured time, given that there has been no event in the first 3 minutes)? (c) (7 points) What is the median interdecay time? (d) (9 points) Let X1 represent the first interdecay time. Use LoUS to write down an integral expression for Ele ], where t is some fixed real number (constant)