The game AceyDeucey a variant of Backgammon derives its name

The game Acey-Deucey (a variant of Backgammon) derives its name from the outcome the pair (1,2) or (2,1) with 2 ordinary 6-sided dice. On any individual roll what is the probability of the event E = {(1.2), (2,1))? If X is the random variable that models the number of rolls a player takes to achieve; (including the roll on which the player is successful), what is the distribution of X? On average how many consecutive rolls can a player expect that it will take in order outcome in E (including the roll on which the player is successful). An insurance company offers its policyholders a number of different payment options selected policyholder let Y = the number of months between successive payments. The distribution function (cdf) of Y is as follows:

Solution