A certain machine has the following hazard function: It is a piece wise function

h(t) = .002 0 < t less than or equal to 200 ; = .001 t > 200

This corresponds to a situation where a device with an exponentially distributed lifetime is replaced after 200 h of operation by another, better device also having an exponential lifetime distribution.

(a) Determine and graph the reliability function.

(b) Determine the probability density function of the machine's lifetime.

(c) Find the mean time to failure.