Length of life of a halogen bulb. For a certain type of halogen light bulb, an old bulb that has been in use for a while tends to have a longer life than a new bulb. Let x represent the life (in hours) of a new halogen light bulb and assume that x has an exponential distribution with mean u = 250 hours. According to Microelectronics and Reliability (January 1986), the “life” distribution of x is considered new better than used (NBU) if P1x 7 a + b2 … P1x 7 a2P1x 7 b2 Alternatively, a “life” distribution is considered new worse than used (NWU) if P1x 7 a + b2 Ú P1x 7 a2P1x 7 b2

a. Show that when a = 300 and b = 200, the exponential distribution is both NBU and NWU.

b. Choose any two positive numbers a and b and repeat part

a. c. Show that, in general, for any positive a and

b, the exponential distribution with mean u is both NBU and NWU. Such a “life” distribution is said to be new same as used, or memoryless. Explain why.