111 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 (Jan.

1986), the “life” distribution of x is considered new better than used (NBU) if

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.

Transcribed Image Text:

P(xa+b) P(x > a)P(x > b) Alternatively, a "life" distribution is considered new worse than used (NWU) if P(x > a+b) P(x > a)P(x > b)