A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 200 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let 
, i = 1,..., 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.
a. Find P(
> 100).
b. Find P(
> 100 and 
> 100 and... and 
> 100).
d. Find P(T ? 100).
e. Let t be any positive number. Find P(T ? t), which is the cumulative distribution function of T.
f. Does T have an exponential distribution?
g. Find the mean of T.
h. If there were n lightbulbs, and the lifetime of each was exponentially distributed with parameter ?,what would be the distribution of T?
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