The maintenance manager at a chemical facility knows that the days between repairs for a specic chemical reactor, denoted by the random variable Y , are well modeled by the distribution with density:
f(y)=0.05e^-0.05y
a. What is the probability that she will need to wait less than 30 days?
b.What is the probability that a repair will be needed sometime after the next 15 days?
c.Given that the chemical reactor has remained operational for the past 50 days, what is the probability that it will fail within the next 50 days?