Problem 3 Random variable represents the number of hours that a machine component will last, and its pdf is () = for 0.

a) Find the probability that the component will last at least 6 hours.

b) The machine has 3 components. Find the probability that they all will last at least 6 hours, assuming that they operate independently.

Problem 4 Random variable has density () = 1 2 || .

a) Sketch the graph of ().

b) Find (|| < 4).

Problem 5 Pick a number at random between 2 and 7.

a) Find the probability that the number is exactly 4.

b) Find the probability that the number is approximately equal to 4.