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A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean...

A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 195 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let XiXi , i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.

Find P(T ≤ 100).

Find P( X1X1 > 100 and   X2X2 > 100 and • • • and   X5X5 > 100)

Find the mean of T .

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Answer:

Find P( X1 > 100 and   X2 > 100 and • • • and   X5 > 100) :

Find P(T ≤ 100) :

Find the mean of T :

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