Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Probability Distributions01:32

Probability Distributions

The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Probability Laws01:49

Probability Laws

Overview
Binomial Probability Distribution01:15

Binomial Probability Distribution

A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
Punnett Squares01:00

Punnett Squares

Overview
Punnett Squares01:00

Punnett Squares

Overview
Law of Independent Assortment02:03

Law of Independent Assortment

While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Reliability of a nonlinear fluctuation-dissipation relation as a test of Markovianity.

Physical review. E·2026
Same author

Hitting the blinking target under stochastic resetting.

Chaos (Woodbury, N.Y.)·2026
Same author

Universalities in a constrained motion of a particle with memory friction: A bead of a Rouse chain on a periodic wire.

Physical review. E·2026
Same author

Camera-based bi-axial measurement of weak forces generated by freely moving plant organs.

Journal of experimental botany·2025
Same author

Souvenir collector's walk: The distribution of the number of steps of a continuous-time random walk ending at a given position.

Physical review. E·2025
Same author

Comment on "Main role of fractal-like nature of conformational space in subdiffusion in proteins".

Physical review. E·2025
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Related Experiment Video

Updated: May 25, 2026

Frequency and Distribution of Crossovers in Caenorhabditis elegans Meiosis by SNP Genotyping using Real-time PCR
06:18

Frequency and Distribution of Crossovers in Caenorhabditis elegans Meiosis by SNP Genotyping using Real-time PCR

Published on: July 11, 2025

Unequal twins: probability distributions do not determine everything.

Yasmine Meroz1, Igor M Sokolov, Joseph Klafter

  • 1School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel Aviv 69978, Israel. merozyas@post.tau.ac.il

Physical Review Letters
|January 17, 2012
PubMed
Summary
This summary is machine-generated.

Knowing the probability distribution function (PDF) of a stochastic model over time is not enough to define all its characteristics. This study demonstrates that two anomalous diffusion models with identical PDFs exhibit different behaviors in other key properties.

Related Experiment Videos

Last Updated: May 25, 2026

Frequency and Distribution of Crossovers in Caenorhabditis elegans Meiosis by SNP Genotyping using Real-time PCR
06:18

Frequency and Distribution of Crossovers in Caenorhabditis elegans Meiosis by SNP Genotyping using Real-time PCR

Published on: July 11, 2025

Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Stochastic models are widely used to describe complex systems.
  • The probability distribution function (PDF) is often considered a complete descriptor of a stochastic model's behavior over time.
  • Anomalous diffusion, deviating from standard Brownian motion, is observed in various physical and biological systems.

Purpose of the Study:

  • To challenge the assumption that the PDF fully characterizes a stochastic model.
  • To compare two distinct exactly solvable models of anomalous diffusion.
  • To highlight differences in model properties beyond the PDF.

Main Methods:

  • Analytical comparison of two exactly solvable anomalous diffusion models: the comb model and the random walk on a random walk.
  • Exact solution of the probability distribution functions (PDFs) for both models.
  • Analysis of other statistical properties including first passage time distributions, autocorrelation functions, and aging properties.

Main Results:

  • Both the comb model and the random walk on a random walk model exhibit identical probability distribution functions (PDFs) over time.
  • Despite having the same PDFs, the two models display significant differences in their first passage time distributions.
  • The autocorrelation functions and aging properties also differ between the two models, indicating distinct dynamical behaviors.

Conclusions:

  • The probability distribution function (PDF) alone is insufficient to fully characterize a stochastic model.
  • Geometric constraints in anomalous diffusion can lead to models with identical PDFs but different dynamical properties.
  • A comprehensive understanding of stochastic processes requires the analysis of multiple characteristics beyond the PDF.