Distribution Definition and 1000 Threads

I have a simple AC circuit. For example a battery with a capacitor. In the steady-state the capacitor has the same V of the battery. The wire that connect the two components is a very small cylindrical conductor, so it should have a surface charge distribution. It's that correct ? If no, why ?

Hi, I am doing a past paper but I am kinda stuck on one of the questions. These are the answers I have: 2a. 225/260 = 0.8654 2b. 32/260 * 4/32 = 0.01407 2c. 32/260 * 28/32 + 228/260 * 221/228 = 0.9577 Then for 2d, I have no idea what to do. Am i suppose to draw one of those probability...

Hey! :o I am looking at the following: 1) A machine produces $100$ gram chocolate. Due to random influences, not all bars are equally heavy. From a long series of observations it is known that the mass X of a chocolate is distributed normally with parameters $\mu = 100$g and $\sigma = 2.0$g...

Homework Statement Derive the bernoulli binomial distribution.Homework EquationsThe Attempt at a Solution Each bernoulii trial could have only two possible outcomes . Let’s name one outcome as success and another outcome as failure. Let’s denote the probability of getting success and failure in...

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...

I am trying to experimentally determine the atomic scattering factors for NaCl using Laue photography. For an NaCl crystal, the intensity of the wave scattered at the unit cell is proportional to (4⋅(fCl+fNa))2 if h,k,l are even and to (4⋅(fCl-fNa))2 if h,k,l are odd. fNa and fCl are the atomic...

Homework Statement I'm asked to find the P (T < ?? ) , v= 26 , α = 0.005 2. Homework Equations The Attempt at a Solution From the table , we could notice that P (T > 2.779) , v= 26 , α = 0.005 , So , i think the ans should be P (T < -2.779 ) , v= 26 , α = 0.005 , But the ans is P (T <...

Homework Statement I have f(x) = BxB-1e-x^B I need to show that E(Xr) = Ƭ(Gamma)(R/B + 1) Homework Equations I know that E(Xr) = f(x) The Attempt at a Solution Attempt at part of solution I started by saying let u = xB so du = BxB-1dx Can I say then that if u = xB, then Xr = ur/B...

Hello, I am reading a review on weak gravitational lensing (https://arxiv.org/pdf/astro-ph/0509252.pdf) and they define the center of an image as follows: $$\vec \theta_c = \frac{\int d^2 \theta I(\vec \theta) q_I [I(\vec \theta)] \vec \theta}{\int d^2 \theta I(\theta) q_I[I(\vec \theta)]}$$...

Hey, I'm attempting to plot a far-field intensity distribution using theoretical values, however I'm having difficulty with calculating the intensity using the following equation: $$I = I_o \frac {sin^{2}{b}}{b^{2}} \frac {sin^{2}{Ny}}{sin^{2}{y}}$$ where: $$y = \frac {kdX}{2f}$$ $$b =...

Homework Statement Let $$ \it{f}(x) $$ be a probability density function. Now let Xn have the density: $$ \it{f}_{n}(x) = n\it{f}(nx) $$ Determine whether or not Xn converges in distribution to zero. (this is the verbatim statement, there is no additional information given)Homework...

Hey! :o Let $M$ be a measure space and $(a_i)_{i\in \mathbb{N}}\subset M$. I want to show that for positive $p_1, \ldots , p_n$ with $\displaystyle{\sum_{i=1}^np_i=1}$ by $\displaystyle{Q=\sum_{i=1}^np_i\delta_{a_i}}$ a probability distribution is defined. Do we have to show that...

Homework Statement part b of below [/B] Homework Equations ##(1+x)^{1/2}=1+\frac{1}{2}x-\frac{x^{2}}{8}+...## The Attempt at a Solution [/B] ##\int\limits^{\Lambda}_{-\Lambda} \frac{dy}{\sqrt{r^2+y^2}}=log(\lambda+\sqrt{\lambda^2+r^2}) - log(-\lambda+\sqrt{\lambda^2+r^2}) ## ##=...

1. The problem statement, all variables, and given/known data I am given a distribution function f(x) that tells me the number of objects with a certain physical property x (such as having a certain mass or temperature) and I need to calculate the total number of objects, the average value of...

I have proved (8.1). However I am trying to prove that ##\bar{X},X_i-\bar{X},i=1,...,n## has a joint distribution that is multivariate normal. I am trying to prove it by looking at the moment generating function: ##E(e^{t(X_i-\bar{X})}=E(e^{tX_i})E(e^{-\frac{t}{n}\sum_{i=1}^n X_i})## I am...

Homework Statement See attached image (See below) Homework Equations Differential equations. And a combination of discrete & continuous distributions The Attempt at a Solution The Continous Distribution Function (CDF) is given in the question. So I differentiated it with respect to x...

Homework Statement The number of tornadoes per year, in Georgia, has a Poisson distribution with a mean of 2.4 tornadoes. Calculate the probability that in any given year, there will be: (i) At most 2 cases. (ii) At least one case. (iii) Calculate the probability that there will be...

Hello, I have a tennis racquet that has a certain weight distribution that makes it play very well. Due to quality control issues from the manufacturer my second racquet of same make and model has a very different weight profile, making matching difficult. I'd like to determine the weight...

Homework Statement Consider the stochastic matrix P giving the probabilities of non-college educated households having at least one college educated child. \begin{pmatrix} .9 & .25\\ .1 & .75 \\ \end{pmatrix} If there are currently 300,000 college educated households, and 750000 noncollege...

Hi The question is about diseased trees in an area (Poisson process), and states that λ = 15 diseased trees in a km square. I need to calculate expected distance from a point in the square to a diseased tree. Now I thought that this means that P(diseased tree = 0) ~ Po(15) = 3.059 x 10^-7 Or...

Hi, I am doing the following question: https://i.gyazo.com/f2e651334bcbd5f1dcb6d661e4160956.png I have estimated both n and theta. But the part that is throwing me off is what problem could you encounter in estimating n here? My only idea is that it might be something to do with the sample...

Dear all, We were trying to solve the following question but did not quite understand what to do. The question is as follows: The reconstructed invariant mass is usually described by a Gaussian (or Normal) distribution. However, the resolution σ (the width of the distribution) is found to...

Can someone derive: ##\frac{Cov(Z+\Theta),\Theta)}{\sqrt{Var(Z+\Theta)Var(\Theta)}}=\frac{\sigma ^2}{\sqrt{1+\sigma ^2}}## My attempt: Numerator: ##Cov(X,Y)=E[(X-E(X))(Y-E(Y))]=E[(Z+\Theta-\theta)(\Theta-\mu)]## The denumerator is pretty simple: ##\sqrt{(1+\sigma ^2)\sigma ^2}##

1. 2. I'm totally lost on this problem. Tried guessing in several ways but couldn't come up with the right answer.3. Since I was totally mesmerized by this problem, I need someone to solve it and provide explanation of critical steps of the process. Can someone help me?

So in my Physics lab, we divided into groups and our task was to throw darts on a target containing 13 bins. The bins look something like the image below. At the end, our class combined our average, standard deviation, and standard error. I made a Gaussian Distribution and I noticed that the...

If we had a a sample of atoms in thermal equilibrium at a temperature, T, it would approximately follow a Maxwell-Boltzmann distribution and be isotropic. But if we now subject these atoms to a force in one direction (e.g. gravity, perhaps near a dense object), it will take the system out of...

Homework Statement Hi There, I'm having trouble understanding (what I guess should be) a simple concept and so I can't apply it to a project I'm working on (also kind of rusty on torques and mechanics problems) If I have a hinged beam (of uniform weight) and I lift it from one end and stay...

Homework Statement What is the name of the experiment that proved Maxwells distribution of velocities? Homework EquationsThe Attempt at a Solution

Homework Statement Homework EquationsThe Attempt at a Solution I want to ask whether there should be a constant in RHS of (5.8).

Is the potential energy of a symmetric planar (x,y) charge distribution lower than any non symmetric distribution ? from the discussion on Gauss's law and symmetric charge distributions I would think so because the electric field could only be normal to the (x,y) plane in the symmetry case but...

Homework Statement I am not getting the above. Let me calculate the probability of getting 2 successes from 5 Bernoulli trials. There are total 10 possible outcomes as each trial has two possible outcomes. The probability of getting one success is P(S1) = No. of successes / no. of total...

Hey folks, I'm having a little bit of trouble shaking the rust off of my radiometry. I'm projecting a circular beam of some known divergence and power onto a surface angled relative to the center of the beam. Say holding a flashlight, with a cone of half angle θ, at my waist some height h off...

(a) We are told $\displaystyle \begin{align*} \textrm{Pr}\,\left( X < 3 \right) = \textrm{Pr}\,\left( Z < a \right) \end{align*}$, so if $\displaystyle \begin{align*} x = 3 \end{align*}$ and $\displaystyle \begin{align*} z = a \end{align*}$ then we have $\displaystyle \begin{align*} z &=...

Greetings! I'm new here and I think about this place as soon as I see what the statement asks. Homework Statement Considering the volumetric density ρv=(e-2r/r2), figure the total charge (ℚ) of the universe. Homework Equations [/B] ρv=ΔQ/ΔV -> (ΔQ ∝ ΔV) ℚ=∫v ρv dxdydz The Attempt at a...

Even though its possible to keep a bus charged from more than one AC voltage sources, what can be the consequences of doing so? My thoughts: - Assuming thst both the sources have similar (but not equal) phase and magnitude, we can expect small circulating currents. Which brings into question the...

I had learned from a book in a lower class that electric power distribution from the generating station is done in phases. Like in India, we have three phases of power transmission: the red, green and yellow colours distinguish the three phases. I believe the same is the case in any other...

Homework Statement Two conducting spheres having same charge density and with radius “R” & “2R” are brought in contact and separated by large distance. What are their final surface charge densities ? Homework Equations No equation in question. The Attempt at a Solution Tried using the fact...

Let's say 5 masses are arranged on x axis. At x=1, 2kg X=2, 4kg X=3, 6kg X=4, 8kg X=5, 10 kg Obviously, there is a total mass of 30 kgIf the mass is distributed continuously by the function M(x) = 2x, then From x= 0 to x=5, there is 25 kg of mass from the simple integral. WHY IS THERE LESS...

Hey! :o Could you tell me when we take which of the following distributions: -binomial -hypergeometric -geometric -poisson -exponential ? (Wondering)

Homework Statement Suppose that X ~ N(μ,σ). Find a in terms of μ and σ if P(X>a) = 1/3 * P(X ≤a) Homework EquationsThe Attempt at a Solution 1 - P(X ≤a) = 1/3 * P(X ≤a) 3 = 4P(X ≤a) P(X ≤a) = 3/4 Since x0 = μ + σz0 where x0 and z0 are the same percentile for N(μ,σ) and N(0,1)...

I have some data that I want to do simple linear regression on. However I don't have a lot of datapoints, and would like to know the uncertainty in the parameters. I.e. the slope and the intercept of the linear regression model. I know it should be possible to get a prob. distribution of the...

Kind of the basic question of atomic physics is momentum distribution of single electron of ground state hydrogen atom - especially the power in its high-energy tail (HTMD: high-tail momentum distribution), which should have strong impact especially on various scattering experiments. Fock's 1935...

Homework Statement Accidents at a busy intersection follow a Poisson distribution with three accidents expected in a week. What is the probability that at least 10 days pass between accidents? Homework Equations F(X) = 1- e-λx μ = 1/λ The Attempt at a Solution Let x = amount of time between...

Hello, can you help me? In my model, I have to simulate source distribution in two volumetric cells (30 and 31). For example, with a photon source of 356 keV, I have to simulate the distribution according 0.2 (20% in source 30: thyroid without nodule) and 0.8 (80% in source 31: nodule). I use...

1. The problem statement, all variables, and given/known data Suppose you have a wire of length l and a uniform line charge density λ. Find the electric field at the midpoint that is height r above the x-axis Homework Equations (see attached) The Attempt at a Solution To solve, I used the...

Homework Statement An ordinary die is painted red on two sides, white on two sides and blue on two sides. Find the probability we get no reds in 12 rolls of the die. Homework EquationsThe Attempt at a Solution GENERAL QUESTION:[/B] I thought this would be a binomial distribution, but the book...

So I worked through the Boltzmann distribution and got: $$ P\propto e^{\frac{-E}{k_BT}} $$ Where $E$ is the energy. So surely this means the kinetic energy (and therefore speed) of particles is distributed over a Boltzmann distribution. Or in equation: $$ P\propto e^{\frac{-mv^2}{2k_BT}} $$...

I was browsing old threads at Physics Forums, and I came across some information in this thread from 2008 that got my interest. The thread is titled "Child molester avoids prison because he is short." PF member stickythighs wrote the following: "Since the average American man is 5'10", there...

Homework Statement A company allows a maximum failure rate of 1 out of 250,000 parts. To insure this quality goal, failed parts must be how many standard deviations from the mean? Use Excel to solve. Homework Equations z= (X-μ)/σ The Attempt at a Solution Hi! So I'm assuming that this is a...

Hi all, I am not sure this is the right forum, but I guess my question fits better here than in classical physics. I am building a lightweight flooring in my utility room to store some "not very heavy" items. Two years back when my house was being finished, I installed two wooden wall plates...