4. A machine operate only as long as at least 2 of its 3 motors are func- tioning. Each motor independently functions fo

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4 A Machine Operate Only As Long As At Least 2 Of Its 3 Motors Are Func Tioning Each Motor Independently Functions Fo 1 (50.11 KiB) Viewed 70 times

4. A machine operate only as long as at least 2 of its 3 motors are func- tioning. Each motor independently functions for a random amount of time with density function f(t) = te-, t > 0. (a) Explain why Pr{1st of the 3 motors would run for time ~ T} = te dt. (b) What is Pr (2nd of the 3 motors would run for less than time t} ? (c) What is Pr {3rd of the 3 motors would run for more than time t} ? (d) What is Pr the machine would run for time t}? What is the prob- ability density function associated with the duration of time the ma- chine would run?