A ?uidized bed reactor through which chlorine gas ?ows has a temperature probe that fails periodically due to corrosion. The length of time (in days) during which the temperature probe functions is known to be a Weibull distributed random variable X, with parameters β = 10; ζ = 2.
(i) Determine the number of days each probe is expected to last.
(ii) If the reactor operator wishes to run a product campaign that lasts continuously for 20 days, determine the probability of running this campaign without having to replace the temperature probe.
(iii) What is the probability that the probe will function for anywhere between 10 and 15 days?
(iv) What is the probability that the probe will fail on or before the 10th day?