Continuous probability distributions provide theoretical models for the life length of a component (e.g., computer chip, lightbulb, automobile, air-conditioning unit, and so on). Often, it is important to know whether or not it is better to periodically replace an old component with a new component. For example, for certain types of lightbulbs, an old bulb that has been in use for a while tends to have a longer life length than a new bulb. Let Y represent the life length of some component with cumulative distribution function F(y). Then the “life” distribution F(y) is considered new better than used (NBU) if

where F̅(y) = 1 – F(y) (Microelectronics and Reliability, Jan. 1986). Alternatively, a “life” distribution F(y) is new worse than used (NWU) if

a. Consider the density function

Find the “life” distribution, F(y).

b. Determine whether the “life” distribution F(y) is NBU or NWU.

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F(x + y) < F(x)F(y) for all x, y 2 0