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Mon 10 Aug, 2015 09:28 am
Say I work at a building that has two entrances. The one closest to the subway stop (Door 1) can't be opened from the outside, but you can go in if someone happens to be going out and opens the door. Going to the farthest door (door 2) will set you back 150 seconds.
If I model the chances of someone coming out of Door 1 as a bernoulli random variable with probability P. The chances of me being able to go in through Door 1 have a geometric distribution.
However, I don't know what P is.
I want to know what would be the optimal amount of time to wait outside Door 1 before giving up and going to Door 2. That is, for how long should I wait outside Door 1 before I can say with 51% confidence that waiting for someone to come out will take longer than the 150 second walk to Door 2.
Thanks!
@rceballos98,
rceballos98 wrote:I want to know what would be the optimal amount of time to wait outside Door 1 before giving up and going to Door 2.
Trick question: There is no optimal amount of time.
@Thomas,
Oh, I think I misunderstood your question. You
don't know P, and you're sampling the people exiting from entrance 1 to estimate it. That's an interesting one.
@Thomas,
Use the Poisson distribution.
https://en.wikipedia.org/wiki/Poisson_distribution
Solve to obtain λ (the average number of space/time events in the interval )
Use k = 0 (zero people come to open the door from inside during the interval )
And P(X= 0) = 0.51 (the probability)
http://stattrek.com/online-calculator/poisson.aspx
Multiply λ , (the mean of the distribution) by the interval (150 seconds ) to obtain the optimal wait time.
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