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Oct
1
awarded  Supporter
Oct
1
comment The Probability of $k$ events in $n$ systems within some time period
Yes -- $t_{\Delta}$ is basically constant (in reality, it is dependent on the number of lights that are on, but it varies so little it probably doesn't matter). And if I understand your second statement, then yes to that as well. I edited the question with a rephrasing of the problem at the start...hopefully it will be better than my first attempt.
Oct
1
revised The Probability of $k$ events in $n$ systems within some time period
Restatement of problem for clarification.
Sep
30
comment The Probability of $k$ events in $n$ systems within some time period
All lights begin as off.
Sep
30
comment The Probability of $k$ events in $n$ systems within some time period
It might be easier to explain this way: I have $n$ lights that turn on with an average of $s$ seconds between turning on and they stay on for $t_{\Delta}$ before turning off (so exponential distribution with $\lambda=1/s$). A light cannot turn on again until it is turned off, but can turn on and off multiple times. What I would like to know is the likelihood that $k$ lights will be on at the same time in the window I care about ($t_{*}$).
Sep
30
comment The Probability of $k$ events in $n$ systems within some time period
I'm not sure what more you are asking for. The only assumption is that my $n$ systems are properly modeled by $\lambda e^{-\lambda t}$. What I'm looking for is the likelihood that, given $n$ systems, what is the likelihood that $k$ events will happen within some time period of each other.
Sep
30
asked The Probability of $k$ events in $n$ systems within some time period
Nov
29
accepted Probability Two Birthdays are within M Days
Nov
29
awarded  Scholar
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29
revised Probability Two Birthdays are within M Days
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revised Probability Two Birthdays are within M Days
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29
revised Probability Two Birthdays are within M Days
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29
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Nov
29
asked Probability Two Birthdays are within M Days
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