/sci/ - Science & Math

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Anonymous Sat Jan 17 01:41:28 2015 No.7015038 [Reply] [Original]

How does one find the standard deviation of something that has a percentage chance of happening?

Say something has a 1% chance of happening. The average is clearly going to be 100 attempts, but how would I find the variance when I don't exactly have a population to test? I've had to do this twice now, and google has turned up nothing both times. What I've been doing is using python to generate the population, and then using that list to find the variance, but there has to be a formula for this out there somewhere.

>>	Anonymous Sat Jan 17 01:51:59 2015 No.7015045 You're describing a geometric distribution: http://en.wikipedia.org/wiki/Geometric_distribution The mean is 1/0.01 = 100, the standard deviation is <span class="math">\sqrt {1 - 0.01} / 0.01 \approx 99.499 [/spoiler]

>>	Anonymous Sat Jan 17 02:02:58 2015 No.7015052 >>7015045 so mean is 1/p(x) and standard deviation is (1-p(x))^.5 / p(x)? What if I wanted to calculate sigma for attempting to get that 1% 6 times?

>>	Anonymous Sat Jan 17 02:05:50 2015 No.7015054 >>7015045 so mean is 1/p(x) and standard deviation is (1-p(x))^.5 / p(x)? What if I wanted to calculate sigma for attempting to get that 1% n times?

>>	Anonymous Sat Jan 17 02:07:51 2015 No.7015058 >>7015054 >>7015045 Also, more curiosity, why are sigma and the mean nearly the same?

Anonymous Sat Jan 17 02:13:05 2015 No.7015062

>>7015054
>so mean is 1/p(x) and standard deviation is (1-p(x))^.5 / p(x)?
Yes.

>What if I wanted to calculate sigma for attempting to get that 1% n times?
Hypergeometric:
http://en.wikipedia.org/wiki/Hypergeometric_distribution
(btw standard deviation is the square root of the variance)

>>7015058
Because there is an EXTREMELY high deviation. It encompasses nearly all of the probabilities because this particular distribution is so close to being linear (the more linear the distribution the more probability the deviation encompasses).

>>	Anonymous Sat Jan 17 02:14:55 2015 No.7015065 >>7015062 the more uniform the distribution* (meaning it has an equal chance to land on any possible outcome)

>>	Anonymous Sat Jan 17 02:31:04 2015 No.7015082 >>7015065 >>7015062 Thanks for the info, I have bordering on no education in this area, but it's always been really interesting to me (and pretty useful too)

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