A person is given k codes but cannot recall which code opens up the safe box. They select each of the codes in turn, in order to be able to open up the safe box on the first attempt, second attempt, and so forth. Let X be the random variable that represents the attempt number that is the one that is successful in opening the door.

1) Determine the sample space for the random variable X.

2) Determine the probability mass function (PMF) P_X[x] and show its result.

3) Determine the expected value of the random variable X, E[X].

4) Assume now that instead of choosing each code in turn, they just randomly choose a new code during each attempt. In this new scenario, determine the probability mass function (PMF) of getting the first success on attempt x. In this scenario, determine the expected value.