Let X denote the time to failure (in years) of a certain hydraulic component. Suppose th...

Let X denote the time to failure (in years) of a certain hydraulic component. Suppose the pdf of X is

a. Verify that f(x) is a legitimate pdf.

b. Determine the cdf.

c. Use the result of part (b) to calculate the probability that time to failure is between 2 and 5 years.

d. What is the expected time to failure?

e. If the component has a salvage value equal to 100/(4 + x) when its time to failure is x, what is the expected salvage value?