# Distribution Definition and 54 Discussions

The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution

f
(
x
;

x

0

,
γ
)

{\displaystyle f(x;x_{0},\gamma )}
is the distribution of the x-intercept of a ray issuing from

(

x

0

,
γ
)

{\displaystyle (x_{0},\gamma )}
with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero.
The Cauchy distribution is often used in statistics as the canonical example of a "pathological" distribution since both its expected value and its variance are undefined (but see § Explanation of undefined moments below). The Cauchy distribution does not have finite moments of order greater than or equal to one; only fractional absolute moments exist. The Cauchy distribution has no moment generating function.
In mathematics, it is closely related to the Poisson kernel, which is the fundamental solution for the Laplace equation in the upper half-plane.
It is one of the few distributions that is stable and has a probability density function that can be expressed analytically, the others being the normal distribution and the Lévy distribution.

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1. ### I Prove that the tail of this distribution goes to zero

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2. ### Winning and losing distributions

I started by trying to write a normal distribution function for losing and not sure if that is possible.
3. ### B It works but why? (Matching experimental data to a random equation)

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4. ### I Fitting Data to Grafted Distribution

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13. ### B Define if the distribution is normal or not

Hello. I wonder how to see if the distribution is normal or not based on the numbers in the table. I attach the screenshot with the table, and it is written that "the distribution appears to be bimodal", so it appears to have two peaks. I understand the the question sounds silly, but I truly...
14. ### I Total number density of galaxies and problematic expression

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15. ### I Understanding part of the multinomial formula

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16. ### Electric field distribution in the brain

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17. ### I T-distribution, standard error - how to interpret

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18. ### Bayesian Probability Distributions

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19. ### Automotive How to find the uneven weight distribution on 4 wheels

Hello, I am working on a project where I am trying to find the weight distribution on a 4 wheeled vehicle that is traveling diagonally up an incline. You can effectively think of the vehicle as having a pitch and a yaw angle in the body frame. Using an arbitrary location of the total center of...
20. ### Thermodynamic assembly - Statistical Thermodynamics

Homework Statement Consider a model thermodynamic assembly in which the allowed (nondegenerate) states have energies 0, ε, 2ε, 3ε.The assembly has four distinguishable (localized) particles and a total energy U = 6ε. Tabulate the nine possible distributions of the four particles among the...
21. ### "Immortal" jellyfish habitat range, Turritopsis dohrnii?

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22. ### I Hypergeometric Distribution Calculation in Libreoffice

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23. ### Marginal Probability Distribution

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24. ### I What is the significance of calculating the average value of cos?

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25. ### Busy barber problem

Homework Statement A barbershop has two barbers: an experienced owner and an apprentice. The owner cuts hair at the rate of 4 customers/hour, while the apprentice can only do 2 customers/hour. The owner and the apprentice work simultaneously, however any new customer will always go first to the...
26. ### Long-run proportion in state ′A′

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27. ### Computer Server Down Probability

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28. ### Determining relative amounts of work done

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29. ### Non-uniform stress distrubution

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30. ### (Statistics) Blackbody spectrum in terms of wavelength?

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31. ### I Place pieces on a chessboard randomly until 2 are adjacent

I've written a program that simulates placing pieces randomly on an nxn chessboard, one by one until 2 are adjacent. When 2 are adjacent I stop, and I report the number of pieces it took. I've plotted a histogram of the number of pieces it took vs number of occurences just to see what kind of...
32. ### Pressure tensor reduces to scalar pressure for isotropic dis

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33. ### Star/delta transformer - single phase fault on secondary

Homework Statement A three-phase distribution transformer is configured as follows: -primary side = star with solidly grounded neutral -secondary side = delta, grounded via zigzag earthing transformer A single phase-earth fault occurs on the secondary (delta) side of the circuit...
34. ### Pure chance question

I recently had a discussion with someone about Quantum Mechanics. His story was confusing to me but I could detect that he made an error in his thinking which I proceeded to explain : You are trying to reason from the idea that the 'collapse of the wave-function', which precedes the...
35. ### Conditional Expectation of Multiple Independent Random Varia

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36. ### Simple Statistics Question

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37. ### Independent Process Probability distribution

A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the...
38. ### How does surface capacitive touchscreen work in detail?

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39. ### Utility Conductor Sizing

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40. ### The Probability Density of X^2?

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41. ### Obtaining Differential and Cumulative Distribution Frequency

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42. ### I am having difficulty with a Gamma Distribution problem

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43. ### Voltage behavior in UG cables and OH 11 KV distribution lines

i want to know the behavior of voltage in 11 KV underground and OH distribution line at different load conditions i.e. no load-full load ...
44. ### Calculating Pressure Distribution in a Nozzle for Abaqus

Hey all, So I have a small convergent nozzle that I'm modelling in Abaqus and I'm wondering how I could work out the pressure distribution so I can apply the correct load. The problem is I only know the pressure being fed to it by air compressor. Is there a way to use Bernoulli s or some other...
45. ### Finding the bias of a random sample

Homework Statement In a study to estimate the proportion of residents in a city that support the construction of a new bypass road in the vicinity, a random sample of 2025 residents were polled. Let X denote the number in the sample who supported the proposal. To estimate the true proportion in...
46. ### Uniform Distribution Probability

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47. ### Derivation of the Boltzmann distribution (Dr. David Tong)

Hello! Dr. David Tong, in his statistical physics notes, derives the Boltzmann distribution in the following manner. He considers a system (say A) in contact with a heat reservoir (say R) that is at a temperature T. He then writes that the number of microstates of the combined system (A and R)...
48. ### Exponential Distribution Probability

Homework Statement The life times, Y in years of a certain brand of low-grade lightbulbs follow an exponential distribution with a mean of 0.6 years. A tester makes random observations of the life times of this particular brand of lightbulbs and records them one by one as either a success if...
49. ### Probability Conditional Expectation

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50. ### Quick question about normal distributions

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