Question: The repair time (in hours) for a certain machine is a random variable with probability density function f(x) = {xex x > 0 0 x

The repair time (in hours) for a certain machine is a random variable with probability density function f(x) =

{xe−x x > 0 0 x ≤ 0

a. What is the probability that the repair time is less than 2 hours?

b. What is the probability that the repair time is between 1.5 and 3 hours?

c. Find the mean repair time.

d. Find the cumulative distribution function of the repair times.

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