Discrete Distributions The geometric distribution is used to model situations where you are interested in counting th enumber of trials in an experiment until a success occurs. It has one parameter (pi), the success probability in each trial. One simple example is when you roll a die and count the number of rolls you need before you get a 3. If we let X be the number of rolls before you get a 3, X can be modeled as a geometric distribution with success probability 1/6. a) For the dice example above, what are the possible values of X? b) For the dice example above, what is the probability that X = 0? Do not use dgeom or pgem. Explain this from probability arguments. c) FOr the dice example above, what is the probability that X=1? Do not use dgeom or pgem. Explain this from probability arguments. d) For the dice example above, what is the probability that X=2? Do not use dgeom or pgem. Explain this from probability arguments. e) Cars arrive to a toll booth and don't have enough cash to pay in full with probability 0.08. What is the expected number of consecutive cars that arrive and do not have enough cash to pay in full?