The life time X of a component, costing $1000, is modelled using an exponential distribution with...

The life time X of a component, costing $1000, is modelled using an exponential distribution with a mean of 5 years. If the component fails during the first year, the manufacturer agrees to give a full refund. If the component fails during the second year, the manufacturer agrees to give a 50% refund. If the component fails after the second year, but before the fifth year the manufacturer agrees to give a 10% refund.

(a) What is the probability that the component lasts more than 1 year?

(b) What is the probability that the component lasts between 2 years and 5 years?

(c) A particular component has already lasted 1 year. What is the probability that it will last at least 5 years, given it has already lasted 1 year?

(d) If the manufacturer sells one component, what should they expect to pay in refunds?

(e) If the manufacturer sells 1000 components, what should they expect to pay in refunds?

Expert Solution

milcah answered 1 year ago

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