The life time X of a component, costing $1000, is modelled usingan exponential distribution with a mean of 5 years. If thecomponent fails during the first year, the manufacturer agrees togive a full refund. If the component fails during the second year,the manufacturer agrees to give a 50% refund. If the componentfails after the second year, but before the fifth year themanufacturer agrees to give a 10% refund.
(a) What is the probability that the component lasts more than 1year?
(b) What is the probability that the component lasts between 2years and 5 years?
(c) A particular component has already lasted 1 year. What isthe probability that it will last at least 5 years, given it hasalready lasted 1 year?
(d) If the manufacturer sells one component, what should theyexpect to pay in refunds?
(e) If the manufacturer sells 1000 components, what should theyexpect to pay in refunds?
