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At any time, a dog has the probability of p to bark. What's the probability that this dog did not bark in the past T seconds?

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    Sounds like HW...2011-06-03
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    Does "at any time" mean "in any second"? (If it means "in any millisecond", for instance, the answer will be rather different.)2011-06-03
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    The answer is $1$ if $p = 0$, else it is $0$.2011-06-03
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    Dan, I guess you are right. ShreevatsaR's comment explained it.2011-06-03
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    Dan, what would be the "right" hypothesis to consider for this problem (instead of "at any time, a dog has the probability of p to bark")?2011-06-03
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    Elliott, this isn't physics.SE! :)2011-06-03
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    Fine, I'll drop the word "hypothesis" from my vocabulary.2011-06-03
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    I was just suggesting that in mathematics we shouldn't assume time is quantized in any particular way. But actually I was wrong for the same reason! :)2011-06-03
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    Dan, that's not how stochastic processes in continuous time work.2011-06-03
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    Is my humor misunderstood. or is it not funny? After I rigorously inspect it I'll know for sure.2011-06-03
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    I was referring to your first comment. The humor in the second one is appreciated.2011-06-03
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    Related: http://math.stackexchange.com/questions/28088/salt-concentration-as-a-function-of-time/28090#28090 :)2011-06-03

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