Suppose that the lifetimes of radio transistors are independent exponential random variables with…

Suppose that the lifetimes of radio transistors are independent exponential random variables with mean five years. Arnold buys a radio and decides to replace its transistor upon failure two times: once when the original transistor dies and once when the replacement dies. He stops using the radio when the second replacement of the transistor goes out of order. Assuming that Arnold repairs the radio if it fails for any other reason, find the probability that he uses the radio at least 15 years.

 

 

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