Distribution Definition and 1000 Threads

I have a PhD in Molecular Neuroscience but am working on something that requires knowledge of electric field distribution in the brain. I understand that electric field intensity (V/cm) is E=(V1-V2)/d in a theoretical model (between 2 infinite plates, that are parallel and equidistant through a...

Hi, I have a PhD in Molecular Neuroscience but am currently working on something that requires a deeper understanding of electric field distribution in the brain. I joined the forum hoping to be able to discuss this topic with a fellow scientist who specializes in this field.

Okay, so I just found out about the Rayleigh distribution being the radial distribution of a point composed of normal distributed cartesian components. And this is because of the area element, right? But how then can the joint density of the cartesian component's distributions equal that of the...

In the first volume of his lectures (cap 6-4) Feynman presents Maxwell's distribution of velocities of the molecules in a gas. And, referring to the PDF graph he says: "If we consider the molecules in a typical container (with a volume of, say, one liter), then there are a very large number N...

What does this diagram tell us about the distribution of nucleons in the nuclei? - The diagram is from Krane Introductory Nuclear Physics I know that nucleons don't congregate around a central part of a nucleus, but instead have a constant distribution throughout. i.e. The number of nucleons...

I have a posterior probability of $$p_i $$which is based on a Beta prior and some data from a binomial distribution: I have another procedure: $P(E)=\prod_{i \in I} p_i^{k_i}(1-p_i)^{1-k_i}$ which gives me the probability of a specific event of successes and failures for the set of $I$ in a...

Hi Imagine we have a lottery, with chance of winning 1 in 1000 (1/1000). I have made computer simulations in order to find confidence levels for winning. At 1000 bought lottery tickets, the confidence of winning is 64.1% and 2000 bought lottery tickets the confidence of winning is 87.1% By...

Homework Statement Use a (simplified) graph to compare the maximum probability (electron density) of the Radial Distribution Function for the 1s and 2s orbitals. Homework Equations xxx The Attempt at a Solution The rest I don't how to solve.[/B]

I'm simplifying a research question that I have at work. Assuming I have 2 coins each with a different probability of head, let's call heads a success (p). Those are biased coins each with a different p, and I do not know the probability of success of each coin, but I do got a sample: Coin 1 -...

Hi all, I am trying to understand two things from a paper The ratio of a standard normal by the square root of a a chi squared divided by its df ( degrees of freedom) is a t distribution. So 1) What is the dist of square root of Chi squared? I know a normal squared is a chi squared, but a chi...

Hello. Math is not my strongest part, yet, so I will be very grateful for your help and for giving the answer in sort of "plain" English, meaning that it will be great if you don't go too deep into the rabbit hole using difficult terminology, as these distribution issues are truly difficult for...

Hi All I made an experiment where I measured the change of the impedance of a coil when I changed a environment parameter X times. For each change I collected ~20 samples. So I have a table with X lines that represent the number the change of the parameter and 20 columns that represent the...

I am confused about the difference between the two In Griffith's 2.3 The Harmonic Oscillator, he superimposes the quantum distribution and classical distribution and says What I understand for quantum case is that ##|\Psi_{100} (x)|^2## gives the probability we will measure the particle...

I have seen that typically most 110Kv and 330Kv lines around my place have not 4 wires on them (3 phases and one neutral) but rather 7 wires on them, which I suppose is 3 phases x2 which probably means two cables for each phase and a common neutral wire at the top of each post. Now is my...

Hello, I was watching a video on the derivation of the Maxwell-Boltzmann distribution function which would eventually lead to: $$\frac{e^{-\beta \cdot \epsilon_i}}{\sum_{i=0}^n e^{-\beta \cdot \epsilon_i}}$$ To do this, initially, the number of possible permutations ##\Omega## of a total of...

Homework Statement A particle with mass m is moving on the x-axis and is described by ## \psi_b = \sqrt{b} \cdot e^{-b |x|}## Find the probability distribution for the particles momentum Homework Equations ## \Phi (p)= \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^\infty \Psi(x,0) \cdot e^{-ipx} dx##...

Homework Statement Give two reasons why transformers are an important part of the power distribution grid My lessons don't have any information regarding this topic. I have read everything in my lesson and can't find anything to answer this question. please help. thank you

Hello, in some exam questions I've looked at it is stated that the pressure distribution is hydrostatic, even though there is fluid motion. (In these cases the velocity has been constant over the section where the pressure is said to be hydrostatic). Is it really possible to assume that the...

Hey! :o We have that $X$ and $Y$ follow the normal distribution $N(0,1)$ and are independent. Which is the distribution of $(X,Y)$ ? Which is the covariance table of $(X,Y)$ ? Is $(X,Y)$ related to the linear combination of $X$ and $Y$ ? (Wondering)

Hi, Given a smooth distribution of lines in R2, could we assert that there is a unique distribution of curves such that: - the family of curves "fill in" R2 completely - every curve is tangent at every point to one of the smooth distribution of lines

Sorry for the abbreviation in the name, the title has a length limit. Homework Statement Let X be a r.v. with cumulative distribution function F(x) and density f(x) = F'(x). Find the probability density function of a) the maximum of n independent random variables all with cumulative...

Been reading basic stuff about the astrophysics behind the prevalence of various elements, curious at what rate this changes over time. The Milky Way is something like 14 billion years old. At first it was all H and He then heavier elements were created and distributed through supernovae...

I was reading the derivation of Boltzmann distribution using the reservoir model. lets call the reservoir by index R and the tiny system by index A. In the derivation they proposed that the probability for being at energy e (for A) is proportional to the number of states in reservoir. I didn't...

Well, the question is if the well known occupation distribution of the energy levels for fermions does break, which means when it is not valid anymore. The Fermi-Dirac distribution reads: ##\displaystyle f_{FD}(E)=\frac{1}{exp\left({\frac{E-\mu}{k_B T}}\right)+1}## And gives the occupation...

In Vol III, 14-4 and 14-5 of the Feynman Lectures (http://www.feynmanlectures.caltech.edu/III_14.html), Feynman gives a discussion of the p-n junction, in which he derives the diode characteristic equation via a nice, simple and convincing application of the Boltzmann distribution to the...

Hi! I wonder, in the case of elastic reactions with nuclear potential, how go from an angular distribution to an energy distribution? I have relationships on differential angular cross sections for neutron and proton elastic nuclear reations and I would like to transform them into differential...

I am trying to estimate the amplitude of a real signal with a particular frequency and unknown phase. The signal is sampled at a frequency much higher than the Nyquist frequency for the signal. For simplicity, I take an FFT period which is a multiple of the signal period (which conveniently is a...

Hi, I'm struggling with a conceptual problem involving the Fourier transform of distributions. This could possibly have gone in Physics but I suspect what I'm not understanding is mathematical. The inverse Fourier transform of a Cauchy distribution, or Lorentian function, is an exponentially...

I was watching a lecture on youtube about linear regression and there's a section where it had the statement below (written in purple). Does multiplying by sigma rotate the distribution to make it look like x - N(mew, sigma^2)? Mew in this case is 0 so it doesn't shift the distribution.

I want to show that for $F_2(t):=\exp\bigg(-\int_t^\infty (x-t)q(x)^2dx\bigg)$, where $q(t)$ satisfies the ODE and the asymptotic relation respectively: $q''=tq+2q^3$ $q(t)\sim Ai(t)$ as $t\to \infty$; and $Ai(x)$ is Airy function such that for $x>0$...

Homework Statement 12 non-distinguishable attacks from President Snow land in Panem’s 12 districts in a particular week. Assume the attacks are located randomly, with each configuration of attacks equally likely. What is the probability that some district had more than 1 attack? Homework...

Homework Statement The actual question was deriving Bose-Einstein, but I got confused on the F-D example. I'm basically following the method given here. Homework Equations [All taken directly from the above link] Taylor series: The Attempt at a Solution So after that third equation...

Homework Statement two indepedent observations ##X_1## and ##X_2## are made up of the continuous random variable having the probability density function ## f(x)= 1/k##, and ## 0≤x≤k## find a. the cumulative distribution of ##X## b. Find the probability distribution of M, the...

Hi, The figure given below was taken from "Nuclear Systems" by TODREAS and KAZIMI. it shows the effect of neutron reflector on the thermal neutron flux radial distribution. Is this correct? Because it does not show the extrapolated distance. It seems to me that the reflector, somehow...

I've added a screenshot (https://imgur.com/a/isQXZ) and the text below for your convenience. Please show steps if possible to help my understanding. Thank you. Consider a random variable that is Normally distributed, with population mean mu = E [X] and population variance sigma^2 = var [X]...

Hello, What do you think about this article? https://arxiv.org/abs/1502.05850 Why and how do we mesure the Spectral Energy Distribution for quasars? Thanks

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...

Could someone please help me understand how force is distributed across a plane as shown in the attached picture (I don't think I have the vocabulary to clearly describe the problem)? If 100 pounds/kg, for example, were placed point 1, what would the force be at points A, B, C and D? Would the...

Homework Statement In a cylindrical container of radius ## R ## and height ## h \ll R ##, with long axis ## \hat{z} ##, in the presence of gravity acceleration ## \vec{g} = - g \vec{z} ## is contained a neutral ionized gas, whose ions can be described as material points with electric charge ##...

Homework Statement [/B] For a straight wire of length 2L carrying a uniform charge density ##\lambda##, find 1) potential a distance z above the centre 2) electric field E at that point, 3) energy of this charge distribution Homework EquationsThe Attempt at a Solution 1) and 2) I can do...

Hi all, I have the following query: I understand that the "make-up" of momentum probability density ##|\tilde{\Psi}|^2## has an effect on the motion of the spatial probability density ##|\Psi|^2##. For example, a Gaussian ##|\tilde{\Psi}|^2## centred far to the right will cause ##|\Psi|^2## to...

Homework Statement Homework Equations V = IR And R becomes 2(r of one conductor) because of return path. The Attempt at a Solution V minimum is at third junction. At VD Using KVL we get: [/B] Drop at AB = (10 + 20 + 50) * 2 * 0.1 = 16 V Drop at BC = (20 + 50) * 2 * 0.08 = 11.2 Drop at CD =...

Hey! :o We consider the exponential distribution. I want to show that $$\mathbb{P}\left (\left |X-\frac{1}{\lambda}\right |\leq \lambda \right )\geq \frac{\lambda^4-1}{\lambda^4}$$ I have shown so far that \begin{align*}\mathbb{P}\left (\left |X-\frac{1}{\lambda}\right |\leq \lambda \right...

Homework Statement Find the distribution of charge giving rise to an electric field whose potential is $$\Phi (x,y) = 2~tan^{-1}(\frac{1+x}{y}) + 2~tan^{-1}(\frac{1-x}{y})$$where x and y are Cartesian coordinates. Such a distribution is called a two-dimensional one since it does not depend on...

I don't get $$\frac{P[x<X<x+dx|N=n]}{dx}=f_{X|N}(x|n)$$ Can someone derive why? I would believe that $$f_{X|N}(x|n)=\frac{f(x,N)}{p_n(N)}$$ but I don't get how that would be the same. And I don't get that $$\frac{P[x<X<x+dx|N=n]}{dx}=\frac{P[N=n|x<X<x+dx]}{P[N=n]}\frac{P[x<X<x+dx]}{dx}$$ Can...

Homework Statement A dealer has a stock of 6 similar television sets which he rents out to customers on a monthly basis. It is known from past experience of the dealer that the monthly demand for the television sets have a Poisson distribution with mean 3.56 (i) Find the probability that in any...

Hi all, I recently learned the concept of Maxwell's speed distribution and became interested in how to use similar momentum distributions to study the probabilistic motion of a classical free particle. I have done some of my own reading on probabilities and distributions (no formal lessons yet)...

Homework Statement The number of flaws in a plastic panel used in the interior of cars has a mean of 2.2 flaws per square meter of panel . What's the probability that there are less than 20 surface flaws in 10 square meter of panel ? Homework EquationsThe Attempt at a Solution This is a...

The following is a somewhat mathematical question, but I am interested in using the idea to define a set of quantum measurement operators defined as described in the answer to this post. Question: The Poisson Distribution ##Pr(M|\lambda)## is given by $$Pr(M|\lambda) =...

I was modeling current distribution in a component: And I plotted the ##\vec J## to simulate & understand the current distribution throughout the conductor, all the flows make sense, however, at the edge of the conductor like so: Current would distribute all around the area, which is...