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Mr. Jones has N light bulbs illuminating his store and once a year on January 1s

ID: 3360766 • Letter: M

Question

Mr. Jones has N light bulbs illuminating his store and once a year on January 1st he replaces all the bulbs that have burned out. He has found out that on the average one-half of the bulbs will burn out during their first year of operation, one-fourth of the bulbus will burn out during their second year of operation, and the remaining of one-fourth of the bulbs will burn out during the third year.

a) What would you choose as state spaces for a Markov Chain modeling? Derive a general definition for transition probabilities.

b) Mr. Jones is 67 years old and he has been doing this for a long time. Assuming N=2, what will be the expected number of light bulbs one, two and three years old on New Year’s Eve (December 31st) of any year

Explanation / Answer

a) Here in this case the states will be two. FIrst state is the bulb in working condition and another second is the burnt bulb.

T = 1 2 ----> year

1 1/2 1/2

2 1/2 1/2

is the transition matrix.

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