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

32/(x 4)3 for x 0.

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?

101. The completion time X for a certain task has cdf F(x) given by?