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In: Statistics and Probability

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 196 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let Xi, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.
a.
Find P(X1 > 100).
b.
Find P(X1 > 100 and X2 > 100 and • • • and X5 > 100).
c.
Find P(T ≤ 100).
d.
Does T have an exponential distribution?
e.
Find the mean of T . _____ hours

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orchestra answered 1 year ago
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