Question: The time in minutes that it takes a worker to complete a task is a random variable with PDF f(x) = k(2 - |x -

The time in minutes that it takes a worker to complete a task is a random variable with PDF f(x) = k(2 - |x - 2|), 0 ≤ x ≤ 4.
(a) Find the value of k that makes this a valid PDF.
(b) What is the probability that it takes more than 3 minutes to complete the task?
(c) Find the expected value of the time to complete the task.
(d) Find the CDF F(x)
(e) Let Y denote the time in seconds required to complete the task. What is the CDF of Y?

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