Questions tagged [statistics]
The statistics tag has no usage guidance.
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Changing Summation to Integral
This is the text from Reif Statistical mechanics. In the screenshot he changes the summation to integral(Eq. 1.5.17) by saying that they are approximately continuous values. However,I don't see how. ...
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0answers
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What is mean by Dispersion in binomial distribution? [on hold]
What is second moment of a variable about its origin
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1answer
25 views
Monte Carlo importance sampling in statistical physics finite approximation question
I am trying to understand a formula found in "Topics in Current Physics: Monte Carlo Methods in Statistical Physics Springer-Verlag" attributed to L. D. Fosdick methods comp physics 1963. I can't get ...
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0answers
26 views
Probability In a Nuclear Transmutation Question
How much cobalt will form into zinc when you add a mole of the set (3 protons, 3 electrons and 5 neutrons) to the cobalt?
I cannot figure out how to find the probability of creating a certain ...
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1answer
25 views
What's “bimodal” about BEC velocity distributions?
I was just reviewing some papers discussing Bose-einstein condensation, specifically "Creation of a Bose-condensed gas of 87Rb by laser cooling" by Hu et al., and I saw repeated references to the ...
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2answers
45 views
What is the proper way to combine two different errors for the same measurement?
We did an experiment in the lab (regarding magnetic domain walls) that yielded some pictures that we later on analyzed and manipulated in Matlab
(we took an RGB image made it into grayscale one and ...
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1answer
44 views
How does the expectation value of a partial derivative of a random variable make mathematical sense in QM?
In probability theory, I'm familiar with the definition of the expectation value of a random variable $X \colon \Omega \rightarrow \mathbb{R}$ being:
$$ \langle X\rangle= \int_{-\infty}^{\infty} x ...
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0answers
32 views
Landau Theory of fluctuations
With respect to chapter 12 in the book Statistical Physics(Part 1) by Landau and Lifshitz, I am currently stuck at the intepretation of Fluctuation theory that Landau provides.
In the neighbourhood of ...
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0answers
22 views
Interpretation of a CLs exclusion plot
I have some trouble with the interpretation of this plot. The plot on the right shows the CLs values for the SM Higgs boson hypothesis as a function of the Higgs boson mass in the range 110–145 GeV. I ...
2
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1answer
37 views
Error propagation and data linearization
I am fairly new to teaching error propagation to students but came across a question I couldn’t answer myself. Say we have a set of data that produces a parabola. In order to linearize the data and ...
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0answers
25 views
How can I determine, in what extent the fit to experimental data is good in Matlab?
I have experimental spectrum in which y-axis is intensity values, and x-axis is frequency values. Int - array of experimental intensities (y-axis). w - array of frequencies (x-axis). I know the view ...
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7answers
1k views
When to average in the lab for indirect measurements?
I am measuring distance and time to calculate the velocity. I repeat the experiment 10 times. What is better, to first calculate the average of distance and time and then the velocity, or to calculate ...
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0answers
30 views
How to fit mean squared displacement data from nanoparticle tracking analysis?
I am trying to independently analyze raw nanoparticle tracking analysis (NTA) data, but my diffusion coefficients calculated directly from x and y pixel values only moderately correlate with reported ...
0
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1answer
29 views
Reduced Chi-Squared values of 5?
I have plotted a linear plot, all errors seem to be on the line yet my chi squared value is 5.
What does this mean for my results? Could there perhaps be a problem with how they were calculated? I ...
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2answers
55 views
How to calculate the error when multiple measurements are made, each of which has an error?
So if I have made three measurements, measuring the same physical quantity $d$:
$a \pm \Delta a$
$b \pm\Delta b$
$c \pm\Delta c$
and I want to take the average of $a, b$ and $c$ to get the ...
2
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2answers
157 views
The mean of Langevin equation
I have a very basic question regarding the mean of the Langevin equation.
So we have an equation of the form:
$$\dot{v}(t)=-\beta v(t)+ \xi (t)$$
Where $\xi (t)$ is a Gaussian white noise with an ...
0
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2answers
42 views
Definition of continuous distribution (intuitively understanding)
Def: A continuous random variable is not defined at specific values. Instead, it is defined over an interval of values, and is represented by the area under a curve. The probability of observing any ...
3
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1answer
61 views
Propagation of asymmetric error bars [duplicate]
I have two (fully independent) measurements of the same quantity X.
Each of them reports a measurement $X_{\sigma_L}^{\sigma_R}$, where $\sigma_L$ and $\sigma_R$ are the left and right uncertainties (...
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2answers
89 views
Notation in Heisenberg Uncertainty Relation: greater than with tilde: $\gtrsim$
In "The Road to Reality" (pg. 523), Roger Penrose writes:
Heisenberg's uncertainty relation tells us that the product of these
spreads cannot be smaller than the order of Planck's constant, and ...
0
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1answer
39 views
Using probability of camera flash interval to get the probability density equation in Griffith's Quantum Mechanics book
In Griffith's QM, example 1 chapter 1, what is the intuition behind using the probability of camera flash interval to get the probability density equation in terms of "dx".
Griffith says that ...
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1answer
194 views
Are the masses of merging black holes correlated?
LIGO/VIRGO recently released data on observed "gravitational wave transients", mostly BH-BH mergers. The data includes a plot of the primary and secondary mass (the primary mass is defined as the ...
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0answers
32 views
Calculate variance of number of photon counts in detector with second coherence function
Knowing the second coherence function of the light beam that's normally incident to a detector how do can you find the variance of the number of counts $n$ received in the time interval $T$.
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1answer
35 views
How should I find an average for data that randomly fluctuates?
I have data for the temperature of a flame at a given height above the burner. The temperature fluctuates quite a bit (see figure), but there is definitely an "average" value that it tends to ...
2
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1answer
24 views
Propagation of uncertainty for a mean value
During an experiment I had to measure the speed of light $c$ (it's an indirect measurement, because i had $c(x,y,z)$ as a function of some quantities $x,y,z$ I could measure).
I took several measures $...
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1answer
70 views
Problem in measuring uncertainty
While performing an experiment involving a bar pendulum, we had to measure the time period of one oscillation by measuring the time taken for 30 oscillations. There is some confusion regarding ...
2
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1answer
127 views
Estimating standard deviation of radioactive decay [closed]
I recently did a laboratory exercise where we had an amount of silver containing two isotopes. Silver with 108 and 110 neutrons, respectively. Using sensors and software, we measured the amount of ...
2
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2answers
96 views
Formula for combining relative uncertainties [duplicate]
Different sources are giving me different formulae for combining relative uncertainties. One tells me to simply add the relative uncertainties together to get the combined uncertainty while another ...
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0answers
23 views
Correlation function and power spectrum of discrete time Gaussian noise summed with a time delayed version of itself
Suppose we have a process $\zeta(n) = \xi(n) + \xi(n + 1)$ Where $\xi(n)$ is discrete time white noise process, where the values taken at different times are from identically distributed Gaussian ...
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1answer
42 views
Is it possible to estimate the average time until entropy decreases a certain amount?
We all know the classical Joule free expansion experiment for an ideal gas: we trap an ideal gas inside half of a cylinder. Then, we open the door and the gas expands to the whole cylinder. After ...
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1answer
35 views
Random walk with Ammonia molecule [closed]
This question is from Keith Stowe's Introduction to Thermodynamics book under Random walk.
The question is something like this:
I am aware that I am not supposed to post homework questions like this ...
6
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2answers
76 views
Why are the Lyapunov and Lindeberg Central Limit Theorem conditions often satisfied in the real world?
Some background for the question.
I've been trying to understand why so many things have a Gaussian Distribution. There are a lot of questions about this on StackExchange but none of them were ...
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1answer
95 views
Why does taking more readings reduce random error? [closed]
So I was tossing a coin
And I did two experiments
Experiment 1:
Tossing same Coin with no fan with different torque each time and did'nt much care about orientation of the coin, 8 times
I got 5 ...
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3answers
72 views
What happens to a radioactive material's atom when it disintegrates?
Suppose you initial had radioactive $2^n$ atoms (where $n$ is an integer). Now after a number of halflives the number of left out atoms becomes 1. Now what will happen to it will it disintegrate and ...
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1answer
73 views
What causes Lorentzian broadening of X-ray diffraction peaks?
In X-ray diffraction, the pseudo-Voigt model is a combination of Gaussian and Lorentzian distributions, and is often used to model peaks. The form of the peak is often described as
$V(x)$ = (1-$\...
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0answers
16 views
Calculation of error in mean from a sample with systematic errors
I have a sample of $N$ measurements and every measurement has a systematic error associated with the instrument that I use. I need to calculate the mean of that sample and provide an error to go with ...
0
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1answer
81 views
Significant figures in a practical experimental problem [duplicate]
Here is a question that combines uncertainties in measurements and significant figures.
Consider the following results to measure the value of g:
$$g={9.7,9.8,9.7,10.0,10.1,10.3}$$
Then to four ...
5
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2answers
272 views
Why aren't Maxwell-Boltzmann statistics used in general cases?
From Probability Theory Vol. 1 Feller Section 2 Chapter 5:
Maxwell-Boltzaman distribution: consider $r$ indistinguishable balls and $n$ cells. Assuming that all $n^r$ possible placements are ...
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1answer
49 views
What is the significance of a $\chi^2$ analysis?
What is the merit of $\chi^2$ analysis in the laboratory experiments? Why is so much emphasis put on it?
1
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1answer
48 views
Modelling the Z mass
I'm interested in approximating (analytically) the mass distribution of the Z boson, as shown below (numerically/MC):
On-shell, you obviously have a Breit-Wigner distribution; but what about to the ...
0
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0answers
98 views
FFT for data sets without any well defined frequency
I am trying to implement FFT algorithm on a data (density of particles) to obtain structure factor. The problem is that in MATLAB (and probably any DFT algorithm which is out there) the assumption is ...
3
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1answer
94 views
Jackknife estimation of variance very different from expected variance
I was rapidly introduced to the Jackknife procedure for data analysis and I stumbled upon a problem I'm not able to understand.
Let's consider a very simple case: the estimation of the average of a ...
0
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1answer
47 views
Feynman Probability lecture 6 - probability density graph
I'm trying to understand the 6-7 graph in the Feynman lecture 6 on
Probability chapter (6–4) A probability distribution
He says:
"We plot $p(x)$ for three values of $N$ in Fig. 6–7. You will ...
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0answers
16 views
Cosmic variance in the power spectra of random fields
How would one decrease the contribution of cosmic variance contribution to the power spectrum? Wider or deeper surveys?
1
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1answer
56 views
statistical errors associated to Monte Carlo sampling
I have $n$ successive observation $A_\mu $ of a quantity $A$ and I need to understand how the expectation values of the square of the statistical error depends from the autocorrelation time but a ...
0
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1answer
45 views
Adding uncertainties when you cannot make any assumptions about the measurements [duplicate]
From what I read, when adding two $x$ and $y$ measurements with uncertainties $\delta x$ and $\delta y$, the resulting uncertainty is determined by doing:
$$\delta z = \sqrt{(\delta x)^2 + (\delta y)^...
0
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1answer
88 views
What's the meaning of the $\sigma$'s of a particle physics measurement?
In particle physics experiments, one often quotes the result of measurement of an observable with $1\sigma$, $2\sigma$, $3\sigma$ ranges. The experiments typically give a best-fit value with a $3\...
2
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0answers
39 views
About thermal diffusion in air and water
I have a fairly simple question:
Why does heat spread faster in air than in water? For me it is counterintuitive compared to the higher thermal conductivity of water. The only "empirical" answer I ...
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4answers
159 views
How to calculate the percentage error of $e^x$ if percentage error in measuring $x$ is given?
How to calculate the error of $e^x$ if percentage error in measuring $x$ is given?
My attempt: calculate the ln or natural log of given function which we usually do in case of exponential function. ...
1
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1answer
39 views
Unsteady flow measurements - Hydraulics
I will soon conduct some experiments on compound channel in unsteady flow case. The flow velocity will be measured using acoustic Doppler velocity. I'd like to have your thoughts about what I'm ...
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1answer
41 views
What kind of errors does normal distribution account for?
No Experiment can give 100% accurate results and are bound to have some errors and normal distribution gives us an idea of distribution of outcomes, But what errors doees it account for, Are they ...
