# Questions tagged [statistics]

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### Errors when the quantity is an exponent

Errors add up in addition or subtraction. Relative errors add up in multiplication or division. When a quantity is raised to a power, the error is increased by times of the exponent. Now what if the ...
1 vote
51 views

### How to use error propagation formula in equation with inseparable variables?

$$R_i(t) = \frac{\mu_{s,E_i}+\mu_{s,E_0}}{\mu_{s,E_i}-\mu_{s,E_0}} \cdot \frac{e^{-\rho\sqrt2\mu_{s,E_0}}-e^{-\rho\sqrt2\mu_{s,E_i}}}{1-e^{-\rho\sqrt2(\mu_{s,E_0}+\mu_{s,E_i})}}.$$ How do I can find ...
32 views

### Propagation of error from statistical error [migrated]

We have done the determination of protein abundance in two fractions (M and P) in one condition (SP). We've done three biological replicas. The data obtained are: \begin{align*} &\text{SP (...
1 vote
92 views

### Ising model and the axiomatics of Statistical Mechanics

I am revisiting Statistical Mechanics to better understand models of spin glass and was wondering to what extent axiomatics of Stat.Mech. applies to an ensamble of spin configurations. In particular, ...
17 views

### Central Limit Theorem for subsamples [migrated]

I observe a set/realisation of $n$ i.i.d. $\{X_1, X_2, ..., X_n\}$. Because of the Central Limit Theorem, I know that repeating such an observation enough times, the pdf of the mean of such $n$ ...
1 vote
42 views

### What is the optimal measuring time split for limited measuring time between signal+background and background in a Poisson counting experiment?

I’m trying to figure out the best split of time between measuring either background or signal+background in a counting experiment in the case where we have no prior knowledge about the mean signal ...
68 views

### Curve fitting and error propagation for non-independent quantities

I have measurement values $y_\mu$ at times $t_\mu$; the should follow a function $y(t) = f_t \, \cos (\Omega_t\cdot t - \delta)$ where $f_t, \Omega_t$ are slowly varying functions (currently I am ...
50 views

### Distribution sampling from a trajectory

Consider a sequence of random variables $\{X_1, X_2,.., X_n\}$ corresponding to regular measurements of a single observable over time obtained from a laboratory or computer experiment. Assume that the ...
526 views

### How large a closed system does the 2nd law of thermodynamics require?

Does the second law of thermodynamics apply to a single electron in deep space? Or two electrons? Or 100? (assume the electrons are restricted in a finite area) From which point we can start to talk ...
1 vote
101 views

### Mean squared displacement of a particle on a biased random walk [closed]

Given a particle on a 1-D random walk with some drift velocity $\nu_d = \frac{\Delta x_d}{\Delta t}$, the position in at some time step j is given by $$x_j=x_{j-1}+k_j L + \Delta x_d$$ where $L$ is ...
40 views

### Which statistical methods are better than basic random scans for studying and exploring the parameter space of extensions of the standard model?

Given a lagrangian of a new model beyond the standard model, and given a set of constraints, say the oblique parameters for instance and the decay of the higgs boson and some signal strengths and ...