A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 199.0 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let X1, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent. 1. Find P( X1 > 100). (Round the final answer to four decimal places.) 2. Find P( X1 > 100 and X2 > 100 and • • • and X5 > 100). (Round the final answer to four decimal places.) 3. Find P(T ≤ 100). (Round the final answer to four decimal places.) 4. Let t be any positive number. Find P(T ≤ t), which is the cumulative distribution function of T. 5. Find the mean of T. (Round the final answer to two decimal places.)
A light fixture contains five lightbulbs. The lifetime of each bulb is exponentially distributed with mean 199.0 hours. Whenever a bulb burns out, it is replaced. Let T be the time of the first bulb replacement. Let X1, i = 1, . . . , 5, be the lifetimes of the five bulbs. Assume the lifetimes of the bulbs are independent.
1. Find P( X1 > 100). (Round the final answer to four decimal places.)
2. Find P( X1 > 100 and X2 > 100 and • • • and X5 > 100). (Round the final answer to four decimal places.)
3. Find P(T ≤ 100). (Round the final answer to four decimal places.)
4. Let t be any positive number. Find P(T ≤ t), which is the cumulative distribution
5. Find the mean of T. (Round the final answer to two decimal places.)
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