Questions tagged [statistics]
The statistics tag has no usage guidance.
2
votes
1answer
18 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 $...
0
votes
1answer
51 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
votes
1answer
83 views
Estimating standard deviation of radioactive decay [on hold]
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
votes
2answers
53 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 ...
0
votes
0answers
17 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 ...
0
votes
0answers
13 views
Confused about Poisson Distribution [migrated]
In textbooks, the Poisson distribution is given as
$P_\mu(x)=\frac{e^{-\mu} \mu^x}{x!}$.
While in Random Matrix theory, they call this: $P_\mu(x)= \mu e^{-\mu x}$ as Poisson distribution.
Maybe ...
0
votes
0answers
16 views
Computing a 'polygonal loop' diagram
I consider a simple spherical SK model of the type $H = -\frac{1}{2} \sum_{i,j} J_{ij} X_i X_j$, with $J$ symmetric, of sieze $n$.
Suppose I have $p \in \mathbb{N}^*$ (assume $p \ll n$). I want to ...
1
vote
1answer
37 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 ...
0
votes
1answer
30 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
votes
2answers
69 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 ...
-1
votes
1answer
61 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 ...
1
vote
3answers
60 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 ...
1
vote
1answer
35 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-$\...
0
votes
0answers
23 views
What types of properties of a system can be studied from Random matrix theory
As we know, The dynamics of a Quantum System is determined by solving the Schrodinger Equation: $H \psi=E \psi$, Once $\psi$ and $E $ is known, then we can find the expectation value of a operator ...
0
votes
0answers
10 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
votes
1answer
72 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
votes
2answers
187 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 ...
1
vote
1answer
48 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
vote
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
votes
0answers
38 views
Reverse task of a Markov Chain Monte Carlo: How to sample distributions/Hamiltonians if one certain realisation is known?
We know MCMC can be used to sample realisations once a probability distribution(or Hamiltonian from which a probability distribution is derived) is given.
But if one certain realisation is already ...
0
votes
0answers
85 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
votes
1answer
81 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
votes
0answers
13 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
vote
1answer
53 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
votes
1answer
34 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
votes
0answers
34 views
Combining systematic and statistical errors for measurements with different instruments
I was wondering how to obtain the systematical error in the instrument calibration when measuring a quantity with different instruments.
Consider the following problem:
I want to measure the length ...
0
votes
1answer
69 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
votes
0answers
35 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 ...
0
votes
4answers
134 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
vote
1answer
34 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 ...
0
votes
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 ...
0
votes
1answer
57 views
Normalization of Probability distribution [closed]
I need to Know.
Is it a condition that Probability density is bounded between 0 and 1?
0
votes
1answer
17 views
How to estimate errors of experimental values like velocity of a wave which have no theoretical values?
I managed to come up that it would be good to use normal distribution and standard deviation acquired from it since there's no value to compare with. But I have no idea how to proceed. Is there any ...
3
votes
3answers
136 views
What is the difference between $\langle v^2 \rangle$ and $\langle |v|\rangle^2$?
Let us take an example: the ideal gas. I know for example that $\langle v \rangle^2$ is different than $\langle v^2 \rangle$, as $\langle v \rangle=0$ due to no preferred direction.
But know if I ...
-1
votes
2answers
64 views
Quantum Mechanics Testability
Statistics by their very nature are not definitive in their predictions for single events. We can say the probability of getting heads on a coin flip is 1/2, yet we can flip a 1000 coins and they ...
0
votes
1answer
32 views
Poisson statistics in photo detectors
I was wondering how would Poisson statistics be used in a photodetectors to account for the number of events that I'm missing in my experiment.
Say I have a material (scintillator, ...) that emits $n$ ...
0
votes
0answers
19 views
Experimentally determined probability has an “error
Feynman , in the paragraph 6-3 of the first Volume of this lectures, writes that an “experimentally determined” probability has an “error,” and writes ( We have only 2 events)
$$P(H)=\frac{N_{H}}{N}(+...
-1
votes
1answer
76 views
Fractional uncertainty question
Q.
A ball falls freely from rest with an acceleration g. The variation with time t of its displacement s is given by s = 1/2 gt^2. The percentage uncertainty in the value of t is ±3% and that in the ...
0
votes
1answer
100 views
Smallest uncertainty ever achieved in position measurement in QM?
The Heisenberg uncertainty principle states that
$$\Delta x\Delta y\geq\hbar/2$$
Since the magnitude of $\hbar$ is $10^{-34}$ we could measure both $x$ and $p$ with an uncertainty magnitude of $10^{-...
46
votes
7answers
5k views
Are random errors necessarily Gaussian?
I have seen random errors being defined as those which average to 0 as the number of measurements goes to infinity, and that the error is equally likely to be positive or negative. This only requires ...
1
vote
0answers
38 views
Asymmetric uncertainty propagation
I am trying to calculate planet-star mass ratios for a number of observed systems, i.e. $\mu=\frac{m_{planet}}{M_{star}}$. Now, most of the planet masses come with asymmetric errors, e.g. WASP 10 ...
0
votes
0answers
31 views
fluctuating rate-of-strain in homogeneous turbulence
When deriving the Reynolds Averaged Navier Stokes equations we separate the flow variables into an average and fluctuating part as follows
$$u = \bar{u} + u'$$
where $\bar{u}$ is some temporal ...
1
vote
2answers
56 views
A doubt related to Significant Digits
Could someone please explain this statement to me
"Reporting the result of measurement that includes more digits than significant digits is superfluous and also misleading since it would give a ...
0
votes
2answers
111 views
How the last digit in significant figures is considered doubtful?
If a reading of a length on meter rod is 44.6cm with least count of 1mm
And last point of the length is exactly on 44.6 not in between of 44.6 or 44.7
Then how is it doubtful?
0
votes
1answer
267 views
Different units on y-axis
I was just wondering if you can have different units on the same y-axis? For example, if I'm graphing blood flow, oxygen level and skin temperature against time in one graph. I can put temperature on ...
2
votes
2answers
76 views
Simple question about propagation of error/uncertainty
I'm stuck on a seemingly simple question about propagation of error. Say we repeatedly measure the speed of a particle, and we estimate the uncertainty in the measured speed to be 10 percent. What is ...
2
votes
2answers
63 views
Why don't we need to do the error calculations for all the repeated measurements?
This is from John Taylor- "An Introduction to Error Analysis"
The passage asks us to calculate the uncertainty of refractive index n using Snell's Law
$$\sin i=n \sin r$$
The fractional ...
-2
votes
1answer
44 views
On the uncertainty relation of Heisenberg
in the uncertainty relation of Heisenberg
ΔxΔp≥ℏ/2 (1)
why we do not take the minus sign of ℏ/2?
i know from the derivation of this relation that we take the square root in the end so it is should ...
1
vote
1answer
54 views
Statistical error with large number of particles in weak measurements
Consider a measurement process. If $\Delta \pi$ and $\Delta x_n$ is the uncertainty in momentum and position of the measuring device.
Aharonov, Albert, et al. ask us to consider the opposite limit: ...
0
votes
0answers
47 views
Correlations and associativity
Suppose one has a set of data $D$ and a theoretical model $M(A,B,C)$ one wants to fit to it by obtaining the best fitting values of the parameters $A,B,C$, which in principle are free. Plotting the ...
