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2
votes
1answer
126 views

Underlying physical basis of an exponential distribution

My data set of upper atmospheric cloud occurrences $N$ versus their thickness (or optical brightness, say $B$) show an exponential variation over more than two orders of magnitude - that is $N$ varies ...
4
votes
2answers
100 views

What's the physical difference between the quantities $\langle v_{i}v_{j}\rangle$ and $\langle v_{i}\rangle\langle v_{j}\rangle$?

What's the physical difference between the quantities $\left\langle v_{i}v_{j}\right\rangle $ and $\left\langle v_{i}\right\rangle \left\langle v_{j}\right\rangle $? Where $\left\langle ...
2
votes
2answers
112 views

Error in variance

I've been exploring techniques in statistical physics, specifically applying them to spin ices. I'm in the canonical ensemble. By using the fluctuation dissipation theorem you can extract useful ...
2
votes
1answer
224 views

Experimental measurement of volumetric flow rate

The other day I with my team had to measure the volumetric flow rate through a pipe only using a 2000 mm$^3$ volumetric flask and a chronometer. The end of the pipe discharged to the atmosphere. As we ...
0
votes
2answers
71 views

Has anyone studied a statistical scaling law for the universe? [closed]

How do named objects in the universe scale? Is there a predictable curve for an ordered list, say {atom, animal, planet, solar system, galaxy, etc}? Can you then use the analysis to predict when the ...
0
votes
1answer
121 views

What is a long-tailed distribution for physicists?

What is the most common definition of long tailed distribution for physicists? I am looking for definition and examples. Examples should have arguments why the distribution is or is not long tailed. ...
1
vote
1answer
65 views

Initial separation of neutron star/black hole binaries?

How would I go about finding the distribution of initial separations (i.e. the lengths between the centres of mass) of stars that make up binary systems. I am interested in neutron stars and stellar ...
2
votes
2answers
6k views

Physical interpretation of y-intercept in a Current vs Voltage graph

So I collected current and voltage data from a simple circuit with a power source and a resistor, using a multimeter. I created a graph for this data using excel and got the y-intercept (which is ...
2
votes
1answer
351 views

Maxwell-Boltzmann velocity PDF to CDF [closed]

I asked on Math.SE and was advised to try here instead. I need to draw from a Maxwell-Boltzmann velocity distribution to initialise a molecular dynamics simulation. I have the PDF but I'm having ...
1
vote
0answers
84 views

Pareto efficiency and Standard Model parameters

Pareto Efficiency is a well understood concept in economics, which basically is a condition where no one actor could be made better off without some one being made worse off. This condition allows ...
2
votes
0answers
261 views

Probability and probability amplitude [duplicate]

What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the ...
0
votes
1answer
60 views

Statistical error in a regression

I measured some voltage values ($x$) and some corresponding frequencies ($y$). I know that the voltage can only be measured within an uncertainty $\Delta x$. And the uncertainty of $y$ shall be ...
5
votes
2answers
333 views

statistics for photon counts in photomultiplier

It seems that a common statistical model for the count numbers of a photomultiplier is a Poisson distribution whose parameter $\lambda$ equals to the square-root of the number of counts.(e.g. ...
5
votes
2answers
593 views

Averaging decibels

Wikipedia: The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level. If I ...
1
vote
0answers
29 views

Half-Life Question [duplicate]

Possible Duplicate: How do we know that some radioactive materials have a half life of millions or even billions of years? I understand how to calculate decay, but it seems to me that the ...
1
vote
4answers
1k views

Statistics in physics

What are the uses of statistics in physics? I am about to embark upon a study of statistics and I would like to know what the particular benefits I gain in physics.
3
votes
3answers
425 views

How to compute the expectation value $\langle x^2 \rangle$ in quantum mechanics?

$$\langle x^2 \rangle = \int_{-\infty}^\infty x^2 |\psi(x)|^2 \text d x$$ What is the meaning of $|\psi(x)|^2$? Does that just mean one has to multiply the wave function with itself?
2
votes
1answer
132 views

Peak deconvolution [closed]

I need some help understanding how much information I can pull out of this data. I have a sample made up of two materials. Materials A and material B. Then I took a picture of the sample. The two ...
0
votes
2answers
343 views

Microsoft Excel not graphing $x = y^{1/2}$

The experiment was relating the period of one "bounce" when you hang a weight on a spring and let it bounce. I have this data here, one being mass and one being time. The time is an average of 5 ...
-1
votes
1answer
278 views

Fitting of exponential data gives me a constant function [closed]

I conducted an experiment, where a capacitor is discharged over a (big) resistor for $t$ seconds and then the remaining charge is measured with a ballistic galvanometer. The data I have is: ...
1
vote
1answer
139 views

How to interpret a negative failure rate?

In statistical engineering the "hazard rate" of a distribution is defined as: $$r(x)=\frac{f(x)}{1-F(x)}$$ where $f(x)$ and $F(x)$ are the PDF and CDF. Basically $r(x)$ is the odds that, having ...
3
votes
4answers
4k views

What are distinguishable and indistinguishable particles in statistical mechanics?

What are distinguishable and indistinguishable particles in statistical mechanics? While learning different distributions in statistical mechanics I came across this doubt; Maxwell-Boltzmann ...
0
votes
0answers
336 views

Intensity of the diffraction pattern of the double slit

I am trying another approach for my last unanswered question. (Bounty still on for 3 days. Anyone? Please?) Note that this is not the same question but a greatly simplified version concerning a much ...
1
vote
2answers
180 views

What is the Schechter luminosity function's domain of support?

I'm trying to fit a Schechter luminosity function to some data points, but it's not clear from this definition what the domain of support of the PDF should be. I'm familiar with the standard Pareto ...
2
votes
2answers
116 views

What is the relation of the release time of fossil fuel emissions to climate change? [closed]

This question presupposes that The amount of fossil fuels on earth is limited Mankind will burn all of its fossil fuels eventually Based on these presuppositions, the total amount of CO2 released ...
2
votes
1answer
260 views

Coherency matrix of partially polarized light doesn't contain all information on polarization state?

The electric field of quasi-monochromatic, partially polarized light can be expressed by the following random process (Goodman, Statistical optics) ...
2
votes
2answers
226 views

Wave Function Statistical Interpretation vs Oscillation Interpretation

Can the wave function solution to Schrodinger's Equation be interpreted as an oscillation between all possible measurements (obviously with some type of weighting that would describe the shape of the ...
2
votes
1answer
217 views

How do you determine the degree of localization of a wavefunction?

Suppose that there is a wavefunction $\Psi (x,0)$ where 0 is referring to $t$. Let us also say that $a(k) = \frac{C\alpha}{\sqrt{\pi}}\exp(-\alpha^2k^2)$ is the spectral contents (spectral amplitudes) ...
2
votes
0answers
96 views

Randomly sampling a “well-mixed” solution of Brownian particles

I place $N$ Brownian particles in $V$ liters of solution, shake until I assume that the particles are "well-mixed", and sample and randomly sample an $S$ liter volume. What is the probability ...
1
vote
2answers
254 views

How to decide convergence of the ensemble average in a Monte Carlo process

I am simulating electromagnetic scattering off a rough surface. The usual process is to do a Monte Carlo simulation, which is briefly described as follows. Generate a randomly rough surface, and ...
2
votes
2answers
251 views

Average Neighbouring Impurity Separation in a Random 1D chain [closed]

I have a finite and discrete 1D chain (edit: linear chain, i.e. a straight line) of atoms, with unit separation, with a set number of impurities randomly distributed in the place of these atoms in ...
1
vote
1answer
94 views

Computing an average escape distance for a particle

Somewhere in a two dimensional convex bulk of particles (pic related) on a random position a reaction takes place and a particle is sent out in a random direction with a constant velocity $v$. What ...
10
votes
2answers
596 views

Use of Monte-Carlo simulation in High-energy Physics

I've been doing some research into the analysis used in particle physics when determining the significance of a finding (e.g. the recent Higgs candidate was announced as a boson in the 125-126 ...
0
votes
2answers
78 views

What is the minimal set of expectation values I need in a statistical model?

At least if $\vec v$ is really only a one dimensional parameter, measuring all the moments $\langle v^n \rangle_f$ seems to give me all the information to compute $\langle A \rangle_f$ with $A(v)$ ...
3
votes
2answers
810 views

Combining multiple theories with 5 $\sigma$ confidence level

Sadly I am not a physicist but I am interested in the topic. Please have mercy with me if you find my question trivial or dumb. Here it comes: As far I understand physicist express their certainty ...
1
vote
0answers
103 views

polynomial fit and uncertainty [closed]

I am trying to fit a polynomial function by least square method and I want to know the uncertainty on my fitting parameters. In which book can I find a clear answer?
4
votes
3answers
284 views

why the difference between $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ is NOT zero?

Well, the difference between the two expressions $\langle \hat p^2 \rangle_{\psi}$ and $\langle \hat p \rangle_{\psi}^2$ is exactly $\Delta p^2$ , i.e. the squared uncertainty (variance) of the ...
1
vote
1answer
140 views

Lacking of scale and distribution moments

Given a physical random variable x, $E(x)$ and $E((x-<x>)^2)$ defines mean and variance. From a statistical point of view variance represents the statistic error (isn't it?). If variance is not ...
1
vote
0answers
78 views

Fitting of data to a model

Imagine that I have some observable value predicted with a theory for some process to be: $1+a x + b x^2$ and observed value is 1.3 with an error 0.2; a and b are some numerical constants. I also have ...
0
votes
1answer
134 views

The discrepancy between the two values in units of sigmas?

Assuming gaussian error distributions, how to calculate the discrepancy between the two values in units of sigmas?
1
vote
1answer
109 views

Variance of Nested Experimental Uncertainty

I have to find the uncertainty of a quantity $Q$ doing two mean values. For example for a set of parameters I measure ten times $Q$, I obtain a mean value $Q_1$ and variance ${\rm Var}(Q_1)$. Then for ...
3
votes
2answers
4k views

How to combine the error of two independent measurements of the same quantity?

I have measured $k_1$ and $k_2$ in two measurements and then I calculated $\Delta k_1$ and $\Delta k_2$. Now I want to calculate $k$ and $\Delta k$. $k$ is just the mean of $k_1$ and $k_2$. I thought ...
2
votes
1answer
604 views

Is $\sigma$ or $\sigma / \sqrt{N}$ is error of a measurement?

I wonder whether $\sigma$ or $\sigma / \sqrt{N}$ is error of a measurement. When I measure, say $0, 1, -1, 1, -1$, I have a $\sigma = 1$. I just measure $0, 1, -1$, I also have $\sigma = 1$. But in ...
10
votes
3answers
3k views

How to combine measurement error with statistic error

We have to measure a period of an oscillation. We are to take the time it takes for 50 oscillations multiple times. I know that I will have a $\Delta t = 0.1 \, \mathrm s$ because of my reaction ...
3
votes
2answers
214 views

Question about uncertainty

Are $3.43\pm 0.04$ $\frac{\mathrm{m}}{\mathrm{s}}$ and $3.48$ $\frac{\mathrm{m}}{\mathrm{s}}$ within expected range of values? The answer is yes, but I do not clearly see why this is so. I appreciate ...
6
votes
0answers
174 views

What statistical test should I use?

I have two differential cross sections $d\sigma_{1,2}/dM$ ($M$ is some invariant mass) corresponding to different hypothesis. What I want is to calculate how well the appropriate experiment would do ...
3
votes
3answers
485 views

Calculating uncertainties for a final result

Say you are dividing 2 times with uncertainties: $$\frac{t_1}{t_2} ~=~ \frac{0.551s \pm 0.002s}{ 0.712s \pm 0.002s}.$$ After doing the calculations you get: $$\frac{t_1}{t_2} ~=~ 0.774 \pm ...
1
vote
1answer
64 views

How to properly read a measurement result if it is a number?

If the result of a measurement is i.e. $3.2 \pm 0.7$, what is 0.7? At which confidence level we know that the real result is inside of this interval?
2
votes
3answers
84 views

Statistics software for basic undergrad lab

I'll have to perform some simple experiments, like measuring the period and damping of a pendulum, focal length of a lens, … As a result I will end up with some X, Y data points and need to calculate ...
1
vote
5answers
409 views

Are Uncertainties in Measurements Important?

In the first lecture of MIT's Classical Mechanics Prof. Lewin highlights the importance of uncertainties in measurements by quoting "Any measurements, without the knowledge of uncertainty is ...