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 October 3rd, 2016, 01:23 PM #1 Newbie   Joined: Oct 2016 From: New Jersey Posts: 2 Thanks: 0 Uniform Probabilty I need help in solving this problem. Problem The lifetimes of batteries are independent uniformly distributed random variables over (0,1) month. A device requires 2 batteries to operate. when a battery fails, both batteries in service are replaced and discarded. If you have a total of n batteries, find the mean of the total amount of time that the device can operate.
 October 3rd, 2016, 03:16 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,463 Thanks: 1340 first thing I'd do is treat pairs of batteries as a single entity. $Pr[\text{battery pack life}  October 3rd, 2016, 06:37 PM #3 Senior Member Joined: Sep 2015 From: USA Posts: 2,463 Thanks: 1340 The solution in post #2 is incorrect. The following is correct. Again treat two batteries at a time as a single entity called a pack.$Pr[\text{life of pack}t]^2$In other words in order for the pack to have failed by time$t$both batteries cannot have lasted longer than$tPr[\text{life of pack}>1] = 1-tPr[\text{life of pack}

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