An experiment consists of rolling a pair of (six- sided) dice and observing the sum. This experiment is repeated until the sum of 7 is observed at which point the experiment stops. Let be the random variable which represents the number of times the experiment is repeated. That is, if the first occurrence of {sum= 7} happens on the 5th roll of the dice, then N =5.
(a) Find the probability mass function for the random variable N. That is, find PN (k) = Pr (N= k) for all k.
(b) What is the probability that the experiment proceeds for at least 4 rolls? That is, find Pr (N ≥ 4).