Question: Electrical components of a particular type have exponentially distributed lifetimes with mean 48 hours. In one application the component is replaced by a new one if it fiats before 48 hours, and in cade it survives 48 hours it is replaced by a new one anyway Let T represent the potential lifetime of a component in continuous use, and U the time of such a component in use with the above replacement policy. Sketch the graphs of
a) The c.d.f. of T: b) the c.d.f. of U. is U discrete, continuous, or neither?
b) Find E(U). [Hint: Express U as a function of T.]
c) Does the replacement policy serve any good purpose? Explain.