The time in days between breakdowns of a machine is exponentially distributed with = 0.2. (a)

Question:

The time in days between breakdowns of a machine is exponentially distributed with λ = 0.2.
(a) What is the expected time between machine breakdowns?
(b) What is the standard deviation of the time between machine breakdowns?
(c) What is the median time between machine breakdowns.'
(d) What is the probability that after the machine is repaired it lasts at least a week before failing again?
(e) If the machine has performed satisfactorily for six days, what is the probability that it lasts at least two more days before breaking down?