Distributions Definition and 337 Threads

In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space).For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.5 for X = tails (assuming that the coin is fair). Examples of random phenomena include the weather condition in a future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc.

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  1. tworitdash

    I Parameters of a distribution of a physical variable

    Pardon me if this is a very silly question. Although my research involves a lot of probability distributions, I consider myself a fledgling statistician. When people assign a probability distribution to a variable in a physical process, is it inherently assumed that the parameters of this...
  2. Haorong Wu

    I Calculate limits as distributions

    Hi, there. I am reading this thesis. On page 146, it reads that I do not know how to calculate the limits when they are viewed as distributions. I am trying to integrate a test function with the limits. So I try (##Q## is defined as ##Q>0##) $$\lim_ {r\rightarrow \infty} \int_{0}^\infty dQ...
  3. L

    A Vector analysis and distributions

    In many books it is just written that ##\Delta(\frac{1}{r})=0##. However it is only the case when ##r \neq 0##. In general case ##\Delta(\frac{1}{r})=-4\pi \delta(\vec{r})##. What abot ##\mbox{div}(\frac{\vec{r}}{r^3})##? What is that in case where we include also point ##0##?
  4. kfulton

    Winning and losing distributions

    I started by trying to write a normal distribution function for losing and not sure if that is possible.
  5. J

    A Probability distributions in an ordered set of extracted elements

    Hello, I tried looking for an existing solution for the following problem: "Assume that S is a set of d elements, and R is a total order relation on S. Assume that n elements are randomly extracted from S, and then they are ordered according to R. Which is the probability that in the i-th...
  6. Philip Koeck

    I Strange feature of BE, FD and Boltzmann distributions

    Hi. I've just come across something rather strange, I believe, about the micro-canonical derivation of the BE-distribution (as well as the Boltzmann and FD-distributions). See for example https://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_statistics#Derivation_from_the_microcanonical_ensemble...
  7. ohwilleke

    I Why Do Physicists Use Gaussian Error Distributions?

    David C. Bailey. "Not Normal: the uncertainties of scientific measurements." Royal Society Open 4(1) Science 160600 (2017). How bad are the tails? According to Bailey in an interview, "The chance of large differences does not fall off exponentially as you'd expect in a normal bell curve," and...
  8. M

    I Dependency of phase space generator to differential distributions

    I attatched an example plot where I created the histogram for the differential distribution with respect to the energy of the d-quark produced in the scattering process. My conception is that the phase space generator can "decide" how much of the available energy it assigns to the respective...
  9. H

    Determining electric field using gauss's law--different distributions

    These are the 4 distributions shown, and I have to determine which two distributions (or none at all) can use Gauss's law to determine the electric field. So electric flux = EA = Q/electric constant. Since all of them have charges, I could do something like Q/(A*electric constant) to get the...
  10. I

    Probability distributions using 4 dice

    Let X denote the largest number shown on the four dice. P(X ≤ x) = (x/6)4 , for x = 1,2,3,4,5,6. Complete the following table: x 1 2 3 4 5 6 P(X=x) 1/1296 15/1296 65/1296 175/1296 369/1296 671/1296 The values in red are the answers, I don't understand how the answers were found. Thanks.
  11. redtree

    I Separation of variables for Named Probability Density Distributions

    Given a probability density distribution ##P(\vec{x})##, for what named distributions is the following true: \begin{equation} \begin{split} P(\vec{x}) &= P_1(x_1) P_2(x_2) ... P_n(x_n) \end{split} \end{equation}
  12. Dale

    Insights Posterior Predictive Distributions in Bayesian Statistics

    [url="https://www.physicsforums.com/insights/posterior-predictive-distributions-in-bayesian-statistics/"]Continue reading...
  13. A

    A Convolution of two geometric distributions

    I'm trying to derive the convolution from two geometric distributions, each of the form: $$\displaystyle \left( 1-p \right) ^{k-1}p$$ as follows $$\displaystyle \sum _{k=1}^{z} \left( 1-p \right) ^{k-1}{p}^{2} \left( 1-p \right) ^{z-k-1}.$$ with as a result: $$\displaystyle \left( 1-p \right)...
  14. S

    I What "space" is used in defining cosmological distributions?

    I assume 3-D cartesian space is not an adequate description for things at the cosmological scale. So what definition of "space" is used when people talk about things like the distribution of hydrogen atoms "in the universe"?
  15. aspodkfpo

    Doppler effect and hydrogen alpha distributions

    https://www.asi.edu.au/wp-content/uploads/2015/03/PhysicsASOE2014solutions.pdf q 14b) i) Assuming that the planet is rotating at a constant rate, shouldn't the distribution be even across all wavelengths, or do I have something very wrong with my model. I take the graph as the summation of...
  16. R

    Maxwell distributions and average, RMS, and most probable speeds

    What I know about a Maxwell distribution is that an area under the distribution on an interval gives the fraction of the molecules with speeds on that interval. My first question is what does Maxwell's distribution represent? It is given by the formula ##P(v) = 4\pi \left(\frac{M}{2\pi...
  17. M

    MHB Maximising the difference between multiple distributions

    I am trying to come up with a parent loss function for the following neural network model. On top of that the algorithm for processing an image would also be helpful. The quad-tree compression algorithm divides an image into ever increasingly small segments (squares) and stops in a particular...
  18. F

    I Estimating decay yields from fits to these distributions

    I'm currently reading various papers on the violation of Lepton Flavour Universality in rare B-decays and I would appreciate some help in understanding the methodology for measuring the ratios in these decays. Here is a quote from a recent paper from the LHCb collaboration (p.5): My question...
  19. wrobel

    A Are there references and do the converse theorems hold for theorems 1,2?

    Hi Colleagues! please look through the enclosed file and I have two questions about theorems 1,2 1) Are there any references? I would prefer to cite these theorems and do not bring proof 2) Do the converse theorems hold?
  20. A

    Projects for Classic Charge Distributions

    In my most recent post, I tried to investigate the V(r) verses “r” for several charge distributions on conductive paper. The discussion there made me realize that the common conductive paper activity is not suitable for doing that. Nevertheless, I am interested in doing projects where I can find...
  21. B

    B How to combine 2 distributions with different sample sizes?

    I apologise in advance for what is a very basic question for someone with a maths degree (it was a long time ago!). I have 2 distributions that look something like this (but with much bigger samples), in the form of (probability,outcome). The outcome is literally just a number. Distribution 1...
  22. Demystifier

    I Why do dark matter and baryon matter have different distributions?

    Dark matter is distributed in halos around visible galaxies, while baryon matter is distributed in spiral-shaped visible galaxies. Where does this difference come from?
  23. M

    A Product of Gaussian and Rayleigh distributions gives what distribution?

    Hello, I'm trying to find out the distribution function (cumulative or density) of the product of two independent random variables respectively following a non-zero-mean Gaussian and a Rayleigh distribution. The math is too intricate for me, I've found in the appendix of [Probability...
  24. J

    Electric Field for Charge Distributions

    We are given: q1 = +2.0 x 10-5 C, q2 = q3 = -3.0 x 10-5 C, r31 = r21 = 2 m a) We start by finding the electric force between q3 to q1 and q2 to q1 FE31 = k * q1 * q3 / r312 FE31 = (9.0 x 109 Nm2/C2) * (+2.0 x 10-5 C) * (3.0 x 10-5 C) / (2 m)2 FE31 = 1.35 N FE21 = k * q1 * q2 / r212 Since...
  25. H

    I Predictions using unknown probability distributions

    My question requires a little bit of background so I will start with that. In a game that focuses on the Pacific Theater of War during WWII, you have two sides: the Allies and the Japanese. It is a turn-based game where each player gives their orders for the day and engagements (when opposing...
  26. redtree

    I Covariance of Fourier conjugates for Gaussian distributions

    Given two variables ##x## and ##k##, the covariance between the variables is as follows, where ##E## denotes the expected value: \begin{equation} \begin{split} COV(x,k)&= E[x k]-E[x]E[k] \end{split} \end{equation} If ##x## and ##k## are Foureir conjugates and ##f(x)## and ##\hat{f}(k)## are...
  27. uzi kiko

    A Estimate the source of a variable when there are several distributions

    Hello everyone In my study, I inject a different amount of fluid in each experiment, such as 1 ml, 2 ml..., and test the change in the general dielectric properties of the solution. Now that I have done much (over 100) measurements for each injection in a specific volume, one can see that for...
  28. L

    I Expectation value of the occupation number in the FD and BE distributions

    In the derivation of the Fermi-Dirac and Bose-Einstein distributions, we compute the Grand Partion Function ##Q##. With ##Q##, we can compute the espection value of the occupation number ##n_{l}##. This is the number of particles in the same energy level ##\varepsilon _{l}##. The book I am...
  29. W

    I Are There Any Theorems Relating Joint Distributions to Marginals?

    Hi all, I was wondering if there exist any theorems that allow one to relate any joint distribution to its marginals in the form of an inequality, whether or not ##X,Y## are independent. For example, is it possible to make a general statement like this? $$f_{XY}(x,y) \geq f_X (x) f_Y(y)$$...
  30. W

    Probability theory: Understanding some steps

    Homework Statement Hi all, I have some difficulty understanding the following problem, help is greatly appreciated! Let ##U_1, U_2, U_3## be independent random variables uniform on ##[0,1]##. Find the probability that the roots of the quadratic ##U_1 x^2 + U_2 x + U3## are real. Homework...
  31. Jarvis323

    A Similarity between -/+ weighted distributions

    Suppose that you have +/- elements aggregated into a weighted distribution function that represents some deviation from an unknown background distribution. What would be a good similarity metric for comparing two such distributions (2D or 3D), if they each represent different perturbations...
  32. B

    MHB Calculating Gadsden Diving Championship Judge Scorecard Distributions

    In the Gadsden Diving Championships there is a panel of three judges. There are 12 scorecards with the numbers 1-12 on them, which are distributed so that each judge has four. After the diver has performed their routine, the judges each hold up a score card, and the diver's score is the sum of...
  33. Cathr

    I Distributions (generalised functions) basics

    I started studying distribution theory and I am struggling with the understanding of some basic concepts. I would hugely appreciate any help, made as simple as possible, because by now I'm only familiar with the formalism, but not all the meaning behind. The concepts I am struggling with are...
  34. dumpling

    A On tempered distributions and wavefunctions

    Very often in standard QM books, certain states, like exponentially growing ones are rejected on the basis that they are not in L^2 space. On the other hand, scattered states are also not in L^2 spaces. This dichotomy can be repelled by using Rigged Hilbert spaces, and allowing tempered...
  35. M

    Charge distributions of two infinite parallel plates

    Homework Statement Two infinitely large conducting plates with excess charge 2Q and 3Q are placed parallel to one another, and at a small distance from one another. How are the charges 2Q and 3Q distributed? You may assume that infinitely large sheets of charge produce electric fields that are...
  36. W

    MHB Solving Point Distributions for Negotiation Simulation w/Thresholds

    I'm trying to create a negotiation simulation and don't know how to find point allocations for each party that will allow agreement in only about 20% of the cases. Wondering whether anyone here would solve the problem for me. The point allocations I came up with allow agreement only a few...
  37. R

    Bayesian Probability Distributions

    Hi, I was having some trouble doing some bayesian probability problems and was wondering if I could get any help. I think I was able to get the first two but am confused on the last. If someone could please check my work to make sure I am correct and help me on the last question that would be...
  38. M

    I Looking for additional material about limits and distributions

    I would like some help to find some additional info on generalized functions, generalized limits. My aim is to understand the strict definition of delta dirac δ(τ).If you could provide a concise tutorial focusing on δ(τ) not the entire theory...it would be of great help. I am not a math...
  39. J

    A Help with this problem of stationary distributions

    I need help with this Consider an irreducible Markov chain with $\left|S\right|<\infty $ and transition function $p$. Suppose that $p\left(x,x\right)=0,\ x\in S$ and that the chain has a stationary distribution $\pi .$ Let $p_x,x\ \in S,$ such that $0<\ p_x<1$ and $Q\left(x,y\right),\ x\in...
  40. J

    Physicist morphed into statistician

    curiosity on distributions related to human characteristics and activity curiosity on fat tailed distributions curiosity
  41. B

    Electric field by continuous charge distributions.

    While reading the book, Electricity and magnetism, the author says that electric field just outside a spherical shell is ##4\pi \sigma##, on it ##4\pi\sigma r_0^2## ,inside is ##0## and outside is ##Q/R^2##. My derivations :- For inside, ##E\Delta S = 4\pi Q = 0## since ##Q = 0##. For...
  42. FallenApple

    A Does Delta Method work for asymptotic distributions?

    So if I have a logistic regression: ##log (\hat {odds})=\hat{\beta_{0}}+\hat{\beta_{1}}x##. How would I find a confidence interval for x if I am given ##odds=5## This is going in reverse, where if I have the outcome, I try to do inference on the predictor. We know that ##\hat{\vec{\beta}}##...
  43. FallenApple

    A Adding Multivariate Normal Distributions

    So ##\vec Y##~MVN(X##\vec\beta##, ##\sigma^2##I) and ##\hat {\vec Y}##~MVN(X##\vec\beta##, ##\sigma^2##H) and I want to show ##\hat{\vec e}##~MVN(##\vec 0##, ##\sigma^2##(I-H)) Where ##\hat{\vec e}## is the vector of observed residuals( ##\vec e=\vec Y- \hat{\vec Y}=(I-H) \vec Y ##). And...
  44. SSequence

    B Probability Distributions (Countably Infinite domain)

    Suppose we have a "particle" which can be at some position x∈N (where N={0,1,2,...}). The probability that the particle is at position x can be written as: P(x) = 1/(2x+1) Now suppose we have two particles p1 and p2.To keep things simple, assume that the individual probability distribution for...
  45. mertcan

    I P(X=x) in continuous distributions

    hi,initially I am aware that for continuous distributions, P(X=x) always equals zero, but when I look at some derivations as the attachment I see that for exponential variable they use exponential pdf when they want to find P(X1=x). My question is : if we say that for continuous distributions...
  46. mertcan

    Prob/Stats Exponential and Poisson distributions or processes

    hi everyone initially I really want to put into words that there is absolutely no source related to following probability in poisson process and distribution $$P(S^1_A<S^1_B<S^1_C)$$ or $$P(S^n_A<S^m_B<S^k_C)$$ where $$S^1_A = \text{first arrival of A event}, S^1_B= \text{first arrival of B...
  47. T

    I Lorenz Curves and Distributions....

    Is it correct to say that the Lorenz curve is the normalized integral of the quantile function with respect to the x-axis?
  48. F

    Gauss's law and symmetric charge distributions

    Having read several introductory notes on Gauss's law, I have found it very frustrating that when the author comes to discussing the standard examples, in which one considers symmetric charge distributions, they do not explicitly discuss the symmetries of the situation, simply stating that, "by...
  49. R

    MHB A question about 'properties of multivariate normal distributions'.

    hello guys, i have a question and looking for an answer quickly... question; prove that, Z is a vector.thank you.
  50. L

    Is temperature measured in kWh normally distributed over different time spans?

    Are the temperature over 24 hours normally distributed? Over 1 year? Over 15 years? Is there a difference in distribution depending on the time span Are MIN temperatures per day i.e. the coldest temperature measured over a 24hr period normally distributed? Over one month Over one year Over 15...
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