Distribution Definition and 1000 Threads

  1. S

    B 4 pounds over the weight limit of a tv stand

    I wanted to put a 39-pound tv on this tv stand: https://www.ikea.com/us/en/p/lack-tv-unit-black-brown-00566060/ The weight limit of top shelf is 35 pounds, but my tv weighs at 39 pounds. Is there any way I can adjust the force distribution so the shelf can hold my tv? tv has 2 base legs about...
  2. S

    B If the source of the pressure distribution around a lifting airfoil is known, why is not explained in textbooks?

    Philosophically, it is impossible to prove a negative, so I will turn to one of the most recognised authorities, Anderson, J. D. (2011) "Fundamentals of Aerodynamics" Fifth Edition. An on-line version can be borrowed from archiv.org at Fundamentals of aerodynamics : Anderson, John D., Jr. (John...
  3. U

    How electricity distributers achieve equal phase loads?

    How electric distributers achieve equal phases load, is this done by itself? Unequal situation hapend only in failure ? That depend on load, not source, but they cant control load.. so how?
  4. ergospherical

    I Calculating the inverse of a function involving the error function

    I have a probability distribution over the interval ##[0, \infty)## given by $$f(x) = \frac{x^2}{2\sqrt{\pi} a^3} \exp\left(- \frac{x^2}{4a^2} \right)$$From this I want to derive a formula for the inverse cumulative density function, ##F^{-1}##. The cumulative density function is a slightly...
  5. D

    Poisson process is identical on equal intervals?

    Let ##N_t## be the Poisson point process with the probability of the random variable ##N_t## being equal to ##x## is given by $$\frac{(\lambda t)^xe^{-\lambda t}}{x!}.$$ ##N_t## has stationary and independent increments, so for any ##\alpha\geq 0, t\geq 0,## the distribution of ##X_t =...
  6. flyusx

    Is a Distribution Function a Ratio of Differentials?

    I read on a post here titled 'Understanding Fourier Transform for Wavefunction Representation in K Space' that if one represents the squared-amplitude as a ratio of differentials, the solution is given. Letting the squared-amplitude be ##\phi##. $$\frac{d\phi}{dp}=\frac{d\phi}{dk}\frac{dk}{dp}$$...
  7. ergospherical

    How Can You Draw from a PDF in Python Without the CDF?

    Some python function f(x) defines an (unnormalised) pdf between x_min and x_max and say we want to draw x randomly from this distribution if we had the CDF F(x) and its inverse F^{-1}(x), we could take values y uniformly in [0,1], and then our random values of x would be x = F^{-1}(y). but...
  8. Elham1990

    News Plot of Parton distribution function

    Hello I plotted the Parton distribution functions in Mathematica. Now I want to compare the graphs drawn with the graphs of other groups(xu and xd). How should I do this?
  9. N

    A Distribution of sum of two circular uniform RVs in the range [0, 2 pi)

    Hello, I would like to know the analytical steps of deriving the distribution of sum of two circular (modulo 2 pi) uniform RVs in the range [0, 2 pi). Any help would be useful Thanks in advance!
  10. hjam24

    I Write probability in terms of shape parameters of beta distribution

    Assume that players A and B play a match where the probability that A will win each point is p, for B its 1-p and a player wins when he reach 11 points by a margin of >= 2The outcome of the match is specified by $$P(y|p, A_{wins})$$ If we know that A wins, his score is specified by B's score; he...
  11. Heisenberg2001

    How is the Maxwell-Boltzmann Distribution Derived?

    1. ##\vec{p}=m\vec{v}## ##H=\frac{\vec{p}^2}{2m}+V=\frac{1}{2}m\vec{v}^2## ##z=\frac{1}{(2\pi \hbar)^3}\int d^3\vec{q}d^3\vec{p}e^{-\beta H(\vec{p},\vec{q})}## ##z=\frac{Vm^3}{(2\pi \hbar)^3}\int d^3 \vec{v}e^{-\beta \frac{mv^2}{2}}## ##z=\frac{Vm^3}{(2\pi \frac{h}{2\pi})^3}\int d^3...
  12. O

    I Is there a Boltzmann distribution for a system with continuous energy?

    Hi. I'm not sure where to put this question, thermodynamics or the quantum physics forum (or somewhere else). For a system in equillibrium with a heat bath at temperature T, the Boltzman distribution can be used. We have the probability of finding the system in state n is given by ##p_n =...
  13. I

    I Radiant Intensity from Radiant Power and Intensity Distribution

    Consider the infrared led TSAL7600 which has the following properties: $$ \Phi = 35 mW $$ $$ I_e = 25 mW/sr $$ The half angle is ## 30^\circ ## and: $$ I_r(\theta) = cos^{4.818}(\theta) $$ is a good approximation for the relative radiant intensity. However, finding the actual radiant...
  14. Z

    I Free particle probability distribution

    Abstract: If a laser shoots photons at a pinhole with a screen behind it, we get a circular non-interference pattern on the screen. Is this distribution Guassian, and if not, what would its wave function be? ===================== Assume a double-slit like experiment, but instead of double...
  15. A

    MCNP FMESH for Plotting power distribution

    Hello I'm trying to use FMESH command to get power distribution of this core geometry. I want to use xyz coordinate in a 1/12 slice of a core so I could use the output of the MCNP sim for a CFD input How should I approach this? Thank you
  16. K

    I Geometric Distribution Problem Clarification

    (Geometric). The probability of being seriously injured in a car crash in an unspecified location is about .1% per hour. A driver is required to traverse this area for 1200 hours in the course of a year. What is the probability that the driver will be seriously injured during the course of the...
  17. C

    Exploring Periodic Distribution of Rigid Balls in a Vast Space

    First of all, all the physical quantities presented in this topic are unknown variables, and I require a functional relationship between these unknown variables. In a vast space that does not consider gravity , there are many ideal rigid balls moving freely. And in equilibrium. The ball is...
  18. shaikh22ammar

    I Casella Berger: Why is distribution of F-statistic in ANOVA not T^2

    Theorem 11.2.8 in Casella & Berger defines the ANOVA statistic as a maxima of T^2 statistic as: \sup_{\sum a_i = 0} T_a^2 = \sup_{\sum a_i = 0} \left( \left( S^2_p \sum a_i^2 / n_i \right)^{-1/2} \left( \sum a_i \bar Y_{i \cdot} - \sum a_i \theta_i\right) \right)^2 = \left( S^2_p...
  19. rogdal

    Gas in a box with Maxwell-Boltzmann distribution

    I have considered two scenarios: 1) A particle that has just collided with the wall at ##z=L## is moving with a velocity ##v_z<0## moving away from the wall. Hence, the probability that this particle has of colliding again is ##0##, so its distribution is also ##0##. 2) A particle moving with...
  20. M

    I Grating Resolving Power of Laser Beams with Gaussian Distribution

    All resources I’ve found for grating resolving power assume uniform distribution on the grating and produce airy disks. Resolvance is determined by the Rayleigh criterion where the peak of one wavelength is at the minima of the adjacent one. This definition doesn’t seem applicable for Gaussian...
  21. F

    B The historical war of currents in Mains Power Distribution: AC vs DC

    So, if I get it right, the basic argument goes like this: AC was preferred to DC because its voltage can be stepped up by a transformer. This limits losses while the current is transported from the production plant to the final user. The voltage is subsequently stepped down when delivered to the...
  22. Frabjous

    I Local dark matter distribution

    We do not seem to have any unexplained orbital/gravitational anomalies within the solar system. What does that imply for the local dark matter distribution?
  23. J

    Derive an expression for the radial charge distribution of an E field

    I know we're supposed to attempt a solution but I'm honestly super confused here. I think the second an third terms of the del equation can be cancelled out because there is only an E field in the r hat direction, so no e field in the theta and phi directions. That leaves us with ##\nabla \cdot...
  24. sol47739

    B Shape & Dimensions of Containers: Impact on the Maxwell Boltzmann Distribution

    1.Does the Maxwell Boltzmann distribution change depending on the shape of the container? Pressure and the volume is constant. How is the Distribution affected whether the gas is in: a,sphere b,cube c,cuboid? Why does/doesn’t the distribution change depending on the shape of the container...
  25. B

    Step down transformers used in residential AC Mains distribution

    Hello, If we have a pole top mounted distribution step down transformer for residential use what happens to the voltage on the secondary side if the primary side voltage increase? Thank you
  26. J

    B Sigma Multiplied Gaussian Distribution

    Hi! Say i have two variables that have independent gaussian distributions of probability of being a certain value when i sample them, what is the likely hood that both will land on a 3 sigma value simultaneously? Is there an equation that easily determines that? Also for other combinations like...
  27. S

    I Is the Boltzmann energy distribution an instance of energy diffusion?

    I (mechanical engineer) have researched this question but can't get to an answer. The equilibrium condition for confined particle diffusion of a solute in a solvent is reached when the solute spatial density is uniform (= zero density gradient), and entropy is max. But per Boltzmann, when...
  28. S

    B Uniform charge distribution in a conductor

    How and why can charge be evenly or uniformly distributed in a conductor? How can such near perfect configuration of charge be achieved? Is outside influence (or force) or any special scientific tools or instruments required to accomplish that? By definition, electrostatic equilibrium is...
  29. C

    I Prove that the tail of this distribution goes to zero

    Theorem: Let ## X ## be a random variable. Then ## \lim_{s \to \infty} P( |X| \geq s ) =0 ## Proof from teacher assistant's notes: We'll show first that ## \lim_{s \to \infty} P( X \geq s ) =0 ## and ## \lim_{s \to \infty} P( X \leq -s ) =0 ##: Let ## (s_n)_{n=1}^\infty ## be a...
  30. chwala

    Understanding the concept of Probability distribution

    Consider the attachment below; How did they arrive at ##F_X (u) = \dfrac{u-a}{b-a}## ? I think there is a mistake on the inequality, probably its supposed to be ##a≤u<b## and that will mean; $$F_X (u) =\dfrac{1}{b-a} \int_a^u du= \dfrac{1}{b-a} ⋅(u-a)$$ as required. Your thoughts...then i...
  31. chwala

    A Finding the Mode of a continous distribution

    Attached is my reference on the literature. My question is; ' are there cases where we may have a continuous distribution that has no Mode value? or is it that the Mode will always be there due to the reason that any given function will have a maximum at some point. Cheers.
  32. J

    A The Probability Distribution of a Bosonic Field when Emitted

    If a bosonic field is probabalistic, and if it can be emitted (suddenly coming into existence), what determines its probability distribution when it is emitted from a fermion? In other words, one thinks (or at least I think) of a fermion field as already being in existence and already having...
  33. A

    A Discrete type normal distribution

    The following is given: $$\displaystyle P(K = k) = \frac{1}{2}~\frac{\sqrt{2}~e^{-\frac{1}{2}~\frac{\left(k -\mu \right)^{2}}{\sigma ^{2}}}}{\sigma ~\sqrt{\pi }}$$ How can you prove that the following equalities are correct? $$\displaystyle \sum _{k=-\infty }^{\infty }1/2\,{\frac {...
  34. A

    A A different discrete normal distribution

    In the article A Discrete Normal Distribution of Dilip Roy in the journal COMMUNICATION IN STATISTICS Theory and methods Vol. 32, no. 10, pp. 1871-1883, 2003 one can read: A discrete normal (##dNormal##) variate, ##dX##, can be viewed as the discrete concentration of the normal variate ##X##...
  35. cosmologyscience

    I Orbital Velocities and Mass Distribution in Galaxies

    Has anyone looked into the details of stellar orbital speeds and required (visible) mass distribution in the Milky Way? Doing some math here - if the local mass density is significantly higher in the inner 10-15% of the galaxy, and then lower and gradually thinning outwards in the disk, we will...
  36. A

    A The distribution that has a certain distribution as its limit case

    I have a probability distribution of the following form: $$\displaystyle f \left(t \right) \, = \, \frac{\lambda ~e^{-\frac{\lambda ~t }{k }}}{k }, \, 0 < t, \, 0< \lambda, \, k = 1, 2, 3, \dots$$ It seems that this distribution is a limiting case of another distribution. The question is what...
  37. SchroedingersLion

    A Covariance of Posterior Predictive Distribution

    Greetings! I believe I found an error in a paper to Bayesian neural networks. I think the expression of the covariance of the posterior predictive is wrong, and I wrote down my own calculation. Would be great if a seasoned Bayesian could take a look. Imagine a regression scenario. We want to...
  38. A

    A The expectation of the sampling distribution of Pearson's correlation

    The shape of the sampling distribution of the Pearson product moment correlation coefficient depends on the size of the sample. Is the expectation of the sampling distribution of the Pearson product moment correlation coefficient always equal to the population correlation coefficient, regardless...
  39. Zuzana

    A LogLikelihood - Poisson distribution

    Hello :) I try to fit some parameters of the particle (e.g. energy, direction) be means of log-likelihood minimization. Input data to likelihood function are pulses amplitudes, while Poisson distribution is used. However, the problem is that Poisson distribution is as follows i.e. for higher...
  40. Rikudo

    Distribution of normal force in this problem

    It is crystal clear that we need torque equation to solve this. But, in order to do so, I need to know where the normal force is located. As far as I'm concerned, normal force is not distributed equally. If this is true, then I suppose this problem is unsolvable? (Though the book says thay it is...
  41. Ranku

    I Mass distribution in a celestial system

    If two sets of objects, of similar size but different mass, were to be part of a rotating celestial system, how differently would they be distributed? Would the distribution of the lower-mass objects be more spread out, while the higher-mass objects would be concentrated toward the centre?
  42. Ranku

    I Celestial Systems: Mass & Distribution

    If two sets of objects, of similar size but different mass, were to be part of a rotating celestial system, how differently would they be distributed? Would the lower-mass objects be more diffusedly distributed, while the higher-mass objects be more concentrated toward the centre?
  43. A

    A How to derive the sampling distribution of some statistics

    Assume that ##T## has an Erlang distribution: $$\displaystyle f \left(t \, | \, k \right)=\frac{\lambda ^{k }~t ^{k -1}~e^{-\lambda ~t }}{\left(k -1\right)!}$$ and ##K## has a geometric distribution $$\displaystyle P \left( K=k \right) \, = \, \left( 1-p \right) ^{k-1}p$$ Then the compound...
  44. WMDhamnekar

    MHB Math Help: Understand How to Compute $F_{X_1}(x)$

    Now, I don't understand how did author compute $F_{X_1}(x) = \displaystyle\sum_{j=1}^n \binom{n}{1} F^1(x) (1-F(x))^{n-1} = 1-(1-F(x))^n ?$ (I know L.H.S = R.H.S) Would any member of Math help board explain me that? Any math help will be accepted.
  45. WMDhamnekar

    A Derivation of P.D.F. from distribution function

    Author computed ##f_{X_k}(x)## as follows but I don't understand it. Would any member explain me the following computations?
  46. chwala

    Solve the problem that involves Normal distribution

    My interest is on part (c), My take, ##Z=\dfrac{160−200}{60}=−0.666666## ##Pr(−0.66666)=0.3546## ##⇒\dfrac{x_1-200}{60}=1.05## ##x_1=63+200=263## Yes, i am aware that they want the answer to ##5## significant figures...i just wanted to check the alternative method... Appreciate your insight...
  47. S

    I Validity of the Boltzmann Distribution

    I (mechanical engineer) have researched this question but can't get to an answer. My question concerns the validity of the Boltzmann distribution. We start with "particles in a box". These particles (at t-zero) may exhibit a range of energies. We place this box of particles in a heat bath for...
  48. A

    A A discrete version of the normal distribution

    I have the following function for the normal distribution: $$\displaystyle f \left(x \right) = \frac{1}{2}~\frac{\sqrt{2}~e^{-\frac{1}{2}~\frac{\left(x -\mu \right)^{2}}{\sigma ^{2}}}}{\sigma ~\sqrt{\pi }}$$ How can the following integrals be equal to their sums? $$\displaystyle \int_{-\infty...
  49. L_ucifer

    Understanding Part (b) of a Charge Distribution Problem

    I understand part (a) of this question, and my answer for that part is: *For r < a* E = (ρ0 * r4) / (6 * ε0 * a3) * For r ≥ a* E = (ρ0 * a3) / (6 * ε0 * r2) Now, for part (b), I understand one solution is, for r < a, find the work done to bring a point charge q from infinity to a and then from...
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