5. The lifetime of a piece of equipment L follows an exponential distribution with mean 1 year. The tax depreciation factor D for writing off the cost of replacing the component after it fails is D =...

Extracted text: 5. The lifetime of a piece of equipment L follows an exponential distribution with mean 1 year. The tax depreciation factor D for writing off the cost of replacing the component after it fails is D = e-L where L is the age of the component in years when it fails and needs to be replaced. The taxable value T of the piece of equipment over its lifetime is then T = v(1 – D) where v is the initial value (cost) of the piece of equipment. What is the expected taxable value over its lifetime of a piece of equipment that initially cost $1000?