A fair die is rolled repeatedly and independently. Let X be the number of rolls until the first time a 5 or 6 has been observed. Note that the trial that 5 or 6 occurred is also counted. Let Y be the number of casts until the first time when both 5 or 6 have been observed.

a) What is the moment generating function of X, Mx(t)

b) What is the moment generating function of Y-X, My-x(t)

c) Find the moment generating function of Y, My(t) and use it to find E(Y)

Help would be greatly appreciated.