Statistical Physics III Problems


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Random variables

The subtlety of statistical independence [nex1]   gif - pdf - ps
Pick the winning die [nex2]    gif - pdf - ps
Gaussian shootist versus Lorentzian shootist [nex3]   gif - pdf - ps
Educated guess [nex4]    gif - pdf - ps
Bertrand's paradox analyzed [nex5]   gif - pdf - ps
Chebyshev's inequality [nex6]   gif - pdf - ps
Law of large numbers [nex7]   gif - pdf - ps
Random variable transformation [nex8]   gif - pdf - ps
Event or complement? That is the question [nex9]   gif - pdf - ps
Random inkjet printer [nex10]   gif - pdf - ps
Win the new car or take a goat! [nex11]   gif - pdf - ps
Random quadratic equations [nex12]   gif - pdf - ps
Three-cornered duel [nex13]   gif - pdf - ps
Reconstructing probability distributions [nex14]   gif - pdf - ps
Binomial distribution and Poisson distribution [nex15]  gif - pdf - ps
Moments and cumulants of the Poisson distribution [nex16]  gif - pdf - ps
Maxwell velocity distribution (Maxwell's derivation) [nex17]  gif - pdf - ps
Random bus schedules [nex18]   gif - pdf - ps
Robust probability distributions [nex19]   gif - pdf - ps
Variances and covariances [nex20]   gif - pdf - ps
De Moivre-Laplace theorem [nex21]   gif - pdf - ps
Pascal distribution [nex22]   gif - pdf - ps
Statistically independent or merely uncorrelated? [nex23]  gif - pdf - ps
Propagation of statistical uncertainty [nex24]   gif - pdf - ps
Bad luck: waiting for the big one [nex74]   gif - pdf - ps
Borel space [nex75]   gif - pdf - ps
Quantity and quality [nex76]   gif - pdf - ps
Diagnosis of a rare deadly disease [nex77]   gif - pdf - ps
Transformation between uniform and Gaussian distributions [nex78]  gif - pdf - ps
Product of independent random variables [nex79]   gif - pdf - ps
Generating exponential and Lorentzian random numbers [nex80]  gif - pdf - ps
Stable probability distributions [nex81]   gif - pdf - ps
Coincident birthdays [nex82]   gif - pdf - ps
Eigenfunctions of linearlized RG transformation for  alpha=2 [nex83]  gif - pdf - ps
Out of Africa [nex84]  gif - pdf - ps
Set identities [nex88]  gif - pdf - ps
Equal events [nex89] gif - pdf - ps
Conditional probability [nex90]  gif - pdf - ps
Successive random picks [nex91]  gif - pdf - ps
Random train connections [nex92]  gif - pdf - ps
Heads or tails [nex93]  gif - pdf - ps 

Stochastic processes

Poisson process [nex25]   gif - pdf - ps
Diffusion process and Cauchy process ar Markov processes [nex26]  gif - pdf - ps
Continuous versus discontinuous Markov process [nex27]  gif - pdf - ps
Markov process for a continuous random variable [nex28]  gif - pdf - ps
Drift equation [nex29]   gif - pdf - ps
Equation of motion for mean value and variance [nex30]  gif - pdf - ps
Fokker-Planck equation for Ornstein-Uhlenbeck process [nex31]  gif - pdf - ps
Jump moments of the master equation [nex32]   gif - pdf - ps
Master equation for random walk in one dimension [nex33]  gif - pdf - ps
Chapman-Kolmogorov equation for biased random walk [nex34]  gif - pdf - ps
Random frequency oscillator [nex35]   gif - pdf - ps
Free particle with uncertain position and velocity [nex36]  gif - pdf - ps
Campbell processes [nex37]   gif - pdf - ps
Life expectancy of the young and the old [nex38]   gif - pdf - ps
Regression theorem for autocorrelation functions [nex39]  gif - pdf - ps
Random walk in Las Vegas [nex40]   gif - pdf - ps
Ornstein-Uhlenbeck process: general solution [nex41]   gif - pdf - ps
Mixing marbles red and white [nex42]   gif - pdf - ps
Remodel the non-Markovian house into a Markovian house [nex43]  gif - pdf - ps
Linear birth-death process [nex44]   gif - pdf - ps
Random light switch [nex45]   gif - pdf - ps
Catalyst driven chemical reaction [nex46]   gif - pdf - ps
Ultracold neutrons in an ideal Steyerl bottle [nex47]   gif - pdf - ps
Air escaping from a leaky container [nex48]   gif - pdf - ps
Air remaining in the leaking container [nex49]   gif - pdf - ps
Master equation yielding Pascal distribution at stationarity [nex50]  gif - pdf - ps
Stationary state for nonlinear birth-death process [nex51]  gif - pdf - ps
Bistable chemical system [nex52]   gif - pdf - ps
Non-differentiability of Wiener process [nex53]   gif - pdf - ps
Autocorrelation function of Wiener process [nex54]   gif - pdf - ps
Detailed balance condition and thermal equilibrium [nex85]  gif - pdf - ps
Random traffic around city block [nex86]   gif - pdf - ps
Modeling a Markov chain [nex87]   gif - pdf - ps
 

Brownian motion

Velocity autocorrelation function of Brownian particle [nex55]  gif - pdf - ps
Mean-square displacement of Brownian particle I [nex56]  gif - pdf - ps
Mean-square displacement of Brownian particle II [nex57]  gif - pdf - ps
Brownian harmonic oscillator I [nex58]   gif - pdf - ps
Brownian harmonic oscillator II [nex59]   gif - pdf - ps
Brownian harmonic oscillator III [nex60]   gif - pdf - ps
Fokker-Planck eq. for Brownian particle: stationary solution [nex61]  gif - pdf - ps
Fokker-Planck eq. for Brownian particle: eigenvalue problem [nex62]  gif - pdf - ps
 

Linear response and equilibrium dynamics

Causality property of response function [nex63]   gif - pdf - ps
Reactive and absorptive parts of linear response [nex64]  gif - pdf - ps
Spectral representations of dynamical quantities [nex65]  gif - pdf - ps
Linear response of classical relaxator [nex66]   gif - pdf - ps
Linear response of classical oscillator [nex67]   gif - pdf - ps
Zwanzig's kinetic equation [nex68]   gif - pdf - ps
Relaxation function with uniform continued fraction coefficients [nex69]  gif - pdf - ps
Critically damped ballistic galvanometer [nex70]   gif - pdf - ps
Structure function of harmonic oscillator I [nex71]   gif - pdf - ps
Structure function of harmonic oscillator II [nex72]   gif - pdf - ps
Structure function of harmonic oscillator III [nex73]   gif - pdf - ps
 
 
Last updated on 12/13/04