B Sigma Multiplied Gaussian Distribution

AI Thread Summary
The discussion centers on calculating the probability of independent Gaussian variables landing within specific sigma ranges. For two variables, the probability of both being within 3 sigma is approximately 0.9948, while for 2 sigma, it is about 0.9109. The formula for determining these probabilities involves using online calculators or tables, with the general equation being (2p)^n for n independent, identically distributed results. The impact of applying a sigma multiplier is unclear, as the formula becomes complex. Overall, understanding these probabilities is crucial for analyzing Gaussian distributions effectively.
jaydnul
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Hi!

Say i have two variables that have independent gaussian distributions of probability of being a certain value when i sample them, what is the likely hood that both will land on a 3 sigma value simultaneously? Is there an equation that easily determines that? Also for other combinations like one at 2 sigma and the other at 3 sigma, or what if i have 3 variables instead of two, etc.

Side question, if i had applied a sigma multiplier of 2x, how does that affect the values?

Thanks!
 
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Prob. of a specific value is 0. Rephrase question - use ranges.
 
jaydnul said:
Hi!

Say i have two variables that have independent gaussian distributions of probability of being a certain value when i sample them, what is the likely hood that both will land on a 3 sigma value simultaneously?
I will assume that you mean within 3 sigma from the mean.
The probability of a result being within 3 sigma is 0.9974. The probability of two independent, identically distributed results being within 3 sigma is 0.9974 * 0.9974 = 0.9948
jaydnul said:
Is there an equation that easily determines that?
The equation for a result being within a certain sigma from the mean is complicated but there are online calculators and tables that you can use. Here is one. It gives you the probability of a result being between 0 and Z, so you would want to double that to include results between -Z and 0. Once you have a probability, ##p##, from the online link and want to use it for ##n## Independent, Identically Distributed (IID) results, the formula is ##(2 p)^n##.
jaydnul said:
Also for other combinations like one at 2 sigma and the other at 3 sigma, or what if i have 3 variables instead of two, etc.
The probability of a result being within 2 sigma is 0.9544. The probability of two independent, identically distributed results being within 2 sigma is 0.9544 * 0.9544 = 0.9109

The probability of three results within 3 sigma is 0.9974 * 0.9974 * 0.9974 = 0.9922
The probability of three results within 2 sigma is 0.9544* 0.9544* 0.9544= 0.8693

jaydnul said:
Side question, if i had applied a sigma multiplier of 2x, how does that affect the values?
It's not clear to me what you mean by a "sigma multiplier". The formula for any number of sigma values is complicated.
 
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