# Questions tagged [statistics]

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### Statistical distribution for “volume exchange”?

The Boltzmann and Gibbs distributions are derived from the assumptions that our system exchanges energy (canonical ensemble) or both energy and particles (grand canonical ensemble) with the ...
0answers
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### Analytical derivation of the distribution of dependent quantities

The problem I am facing is the following. I do have two physical quantities, $x$ and $y$, and I know the analytical relation between the two $$y = g(x)$$ Now, I know that $x$ is well represented by a ...
2answers
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2answers
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### How do you combine the errors resulting from measuring one instrument with another?

In a recent lab, we were asked to find the time constant, $\tau$ by timing the discharge of a capacitor through a resistor. The voltage on the capacitor was measured with a DMM whose instrumentation ...
0answers
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### CMS Paper of Higgs Discovery: Exclusion Plots [duplicate]

In the discovery paper of CMS of the Higgs boson, on page 24, we can find the following plot: Question: What is the dashed line really representing? After all, it says in the caption that this line ...
1answer
35 views

### Is there any significant scale nuclear transmutation currently in practice?

There was a similar question in place but the details of the answer may suggest another solution. So I am aware that transmutation is used to reprocess radionuclides in nuclear waste to render them ...
1answer
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### Calculating basic systematic error

My lab partner and I are in disagreement about what the systematic error of our temperature measurement is. The digital temperature gauge measured to one decimal place (i.e 20.3°C). We took a number ...
20answers
11k views

### How do you make more precise instruments while only using less precise instruments?

I'm not sure where this question should go, but I think this site is as good as any. When humankind started out, all we had was sticks and stones. Today we have electron microscopes, gigapixel cameras ...
1answer
67 views

### What does $\Delta p$ in uncertainty principle mean?

What does the $\Delta p$ in uncertainty principle mean? Is it standard deviation? I have seen few videos on youtube as well as in our high school textbooks, it was proved that the electrons don't ...
3answers
128 views

### What does the $\langle \rangle$ notation mean?

I have what I think is a very simple question, basically, what does the notation "$\langle \rangle$" stand for? My background is in math and I am not familiar with physics notations. I am ...
0answers
35 views

### Decoupling noises

This is an experimental physics problem: Say I have 3 random variables $P_1, P_2, P_3$ such as : $\Delta P_i=\Delta_Q P_i +\Delta_0P_i \ \ \forall i$, where $\Delta$ is the variance, this equations ...
3answers
186 views

### Why do physicists, in quantum mechanics, call average an expectation value, not expected value? [closed]

I guess there is a specific reason for this - calling the expected observation $$\langle\psi|\hat{Q}|\psi\rangle$$ (for a normalised wavefunction) an expectation value. I heard somewhere that, in ...
1answer
76 views

### Exponential rule for propagation of errors

I'm struggling to follow what feels like it should be a simple method. I often see that for if you want to find the error of an exponential, it follows: if $y = x^{n}$ we have \$\frac{\Delta y}{y} = n\...
1answer
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### How to calculate uncertainty of rounded data [closed]

I have been seriously confused with the following text for a short while. Suppose that three teachers have timed the school 100 m sprint race and have recorded times of 12.3, 12.5, and 12.6 s for the ...
1answer
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### How is measurement uncertainty defined / calculated (of a sensor or measurement)?

Textbooks and online sources often say the industry standard for uncertainty is given at a confidence interval of 95 %. This means out of 100 measurements, 95 would achieve the specified value and ...
8answers
14k views

### Can 1 kilogram of radioactive material with half life of 5 years just decay in the next minute?

I wondered this since my teacher told us about half life of radioactive materials back in school. It seems intuitive to me to think this way, but I wonder if there's a deeper explanation which proves ...