probability and statistics for economists

A psychologist has estimated that either 1,2, or 3 hours of examination is required
to properly assess the case of a new patient. Allow X to be a random variable indicating
the time in hours that it takes with a patient to complete this task. The following
probability function has been proposed.
f (x) = x / 6 for x = 1,2 or 3
a) Is this a discrete or a continuous probability function? Explain.
b) Does this function satisfy the axioms of probability? Explain.
c) Give the cumulative density function.
d) Use the cumulative density function to determine the probability that it takes exactly 2
hours to complete the task.