How to Derive Uncertainty from Mean and RMS?

AI Thread Summary
The discussion focuses on deriving uncertainty from the function F = os - ss, where os and ss represent opposite-sign and same-sign binomial distributions. The mean and root mean square (RMS) equations for the function are provided, with the mean calculated as N(total) * (2*prob(os) -1) and the RMS as 2 * SQRT { N(total) * prob(os) * (1 - prob(os)) }. A participant clarifies that RMS is the square root of the variance, confirming the relationship between these statistical measures. The original poster seeks to understand if an equation for variance can be derived from the provided information. The conversation concludes with a confirmation of the relationship between RMS and variance.
penguindecay
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Dear Reader,

Earlier I posted a topic on the uncertainty of a function that is F = os - ss , where os and ss are opposite-sign and same-sign, and are both binomial distributions. I want to know the uncertainty of my F,

I have found a equation for the mean, and rms of my function which are:

N(total) * (2*prob(os) -1 ) for the mean and

2 * SQRT { N(total) * prob(os) * (1 - prob(os)) } for the rms

where N(total) = os+ss

Is it possible to get an equation for the variance or uncertainty from the given information?

Thank you for reading

Kim
 
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I am not sure what you are looking for. However rms is simply the square root of the variance.
 
mathman said:
I am not sure what you are looking for. However rms is simply the square root of the variance.

I am looking for the square root of the variance, and if it is as you state the rms equation I have, then thank you.
 
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

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