1. ## order stat

X is a system that consists of three devices. The system would work correctly if at least one of the device works. Mean time for failure of each device are

beta1 = 75
beta2 = 50
beta3 = 25

life times are exponentially distributed

part a) find the density function for the lifetime of X

2. Originally Posted by ilikec
X is a system that consists of three devices. The system would work correctly if at least one of the device works. Mean time for failure of each device are

beta1 = 75
beta2 = 50
beta3 = 25

life times are exponentially distributed

part a) find the density function for the lifetime of X

You need to find the pdf of $X_{(3)} = \text{max} \, (X_1, \, X_2, \, X_2)$. One approach would be to use the method of distribution functions (which is certain to be explained somewhere in your class notes and textbook).