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Questions tagged [statistics]

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0
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1answer
19 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 ...
1
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2answers
47 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 ...
0
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0answers
18 views

Best method for determining tolerances based on production data [migrated]

Say I am producing a wound coil which is ultimately going to be used in a colpitt's oscillator circuit. I measure the Ls and Rs of the coil, and then install it in a ferrite and then test it in the ...
0
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0answers
41 views

Standard deviation about a value other than the mean [migrated]

We generally define standard deviation to be the deviation of the data points about the mean of the whole set, but why about mean? Couldn't we do it about the RMS value? Or any other value? So I was ...
2
votes
2answers
145 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
41 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
45 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 (...
1
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2answers
85 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
38 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 ...
18
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1answer
189 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 ...
1
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0answers
26 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 $T$.
1
vote
1answer
33 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
votes
1answer
22 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
65 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
101 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
votes
2answers
68 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
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0answers
21 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
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0answers
18 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
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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
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1answer
33 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
72 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
68 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
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3answers
67 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
47 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
24 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
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0answers
11 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
73 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
223 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
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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
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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
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0answers
88 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
87 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 ...
0
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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
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
38 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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0answers
56 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
76 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
37 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
147 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
38 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
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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 ...
0
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1answer
61 views

Normalization of Probability distribution [closed]

I need to Know. Is it a condition that Probability density is bounded between 0 and 1?
0
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1answer
18 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
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3answers
137 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 ...
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2answers
65 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
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1answer
36 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
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0answers
21 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}(+...
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1answer
110 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 ...