Distribution Definition and 1000 Threads

I came across this problem in my assignement but I don't really understand the question. The lectures notes handed out by the teacher does not use the term cumulative distribution. Wikipedia says that a cumulative distribution function is the same as a distribution function.

Hi all. I'm trying to find a formula that will calculate the probability distribution of a stock price after X days, using the assumption that the price change follows a normal distribution. In the spreadsheet, you can see the simulation I've made of the probability distribution of the price of...

Homework Statement A charge of +3.0 μC is distributed uniformly along the circumference of a circle with a radius of 20 cm. How much external energy is required to bring a charge of 25μC from infinity to the centre of the circle? a . 5.4 J b. 3.4 J <- answer c. 4.3 J d. 2.7 J e. 6.8 J=...

How can I calculate ∂/∂t(∫01 f(x,t,H(x-t)*a)dt), where a is a constant, H(x) is the Heaviside step function, and f is I know it must have something to do with distributions and the derivative of the Heaviside function which is ∂/∂t(H(t))=δ(x)... but I don't understand how can I work with the...

Hi, I'm looking for a simple explanation of the meaning of the crow flight distance and why it is defined as the second moment of a probability distribution: $$\bar r^2 = \int r^2 p(r)dr$$ Where ##p(r)## is the probability that a neutron is absorbed in the interval ##dr## near ##r##. And what...

I have been reading about the quantum effects that limit the Maxwell-Boltzmann Distribution under certain conditions which leads to the Bose-Einstein or Fermi-Dirac Distribution. I have difficulty grasping the reasons why these quantum-effects occur only at certain conditions and why exactly...

Hi PF! I am suppose to determine if the following rule is a distribution $$\langle u,\phi \rangle = \int_0^1 \frac{u(x)}{x} \, dx$$ and then also $$\langle u,\phi \rangle = \int_{-\infty}^\infty \phi + 1 \, dx.$$ The notation is throwing me off. At first I thought I had to show ## \langle Au +...

Homework Statement Let ##T## be a distribution in ##\mathcal{D}(\mathbb{R}^2)## such that: $$T(\phi) = \int_{0}^{1}dr \int_{0}^{\pi} \phi(r, \Phi)d\Phi$$ $$\phi \in \mathcal{D}(\mathbb{R}^2)$$ calculate ##r \frac{\partial{}}{\partial{r}} \frac{\partial{}}{\partial{\Phi}}T##. Homework...

Does anybody know if there is an analytical expression for the electrostatic potential produced by a charge distribution confined to a double cone shaped region. Think of a beam of charged particles converging to a focus and then diverging again. The total charge in each thin, cross-sectional...

Hi there, I've got a Heat Transfer problem that I can't seem to get right. I will list all information in the problem without 'interpreting' it: Givens: 100 cm long cylinder filled with hot water, and constantly heated to maintain the water at 100°C. Heat is transferred via conduction from...

Consider a very simple idealized circuit, with a constant voltage emf, perfectly conducting wires and a resistor all in series. There is a potential drop across the resistor, given by Ohm's law: ##V = -IR##. I have read on the Internet that many people say that the potential drop is caused by a...

If X and Y are independent gamma random variables with parameters $(\alpha,\lambda)$ and $(\beta,\lambda)$, respectively, compute the joint density of U=X+Y and $V=\frac{X}{X+Y}$ without using Jacobian transformation. Hint:The joint density function can be obtained by differentiating the...

I can't prove this proposition. I have however managed to prove that the linear combinations of the independent normal rv's are also normal by looking at it's mgf $$E(e^{X_1+X_2+...+X_n})=E(e^{X_1})E(e^{X_2})...E(e^{X_n})$$ The mgf of a normal distribution is $$e^{\mu t}e^{\frac{t^2...

I would like to know the difference between the ##\chi^{2}## distribution and the PTE (Probability-To-Exceed) ? I must compare 2 data sets A and B and in the article I am reading, they talk about this PTE : For the moment, I only know the ##\chi^{2}## distribution with ##k=2## degrees of...

Homework Statement (i) Construct the cumulative distribution table for the number of heads when the four coins are tossed. Coins are fair. (ii) Find the Median.Homework EquationsThe Attempt at a Solution (i) x 0 1 2 3...

Two identical metalic spherical conductor of radii ##R## are at a distance ##d## apart.One of the conductor has charge ##Q## while the another one is neutral.What will be the induced charge on the other conductor ? If we put an image charge ##q## inside the neutral one. Then the potential at...

Hi :) Here's my problem along with what I've done. Here is the problem: That is the p.d.f. of a random variable X. I have to find the cdf. I don't know which I should do so I tried it two ways. First: $\int_{-1}^{1} \ \frac{2}{\pi(1+x^{2})} dx = {{\frac{2}{\pi} arctan(x)]}^{1}}_{-1}=1$...

Dear colleagues I have this problem which I don't understand from where they got the solution I tried to solve it with slot of methods with the same answer which not the stated answer. A point charge (q) is located a distance (b) from a grounded conducting sphere with radius (a) show that the...

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...

Homework Statement Find A in p(x) = Aexp(-λ(x-a)^2) by using the equation 1 = ∫ p(x)dxHomework Equations 1 = ∫p(x)dx The Attempt at a Solution I expand the power of the exponential and then extract the constant exponential to get: Aexp(λa^2) ∫exp(-λx^2)exp(2aλx)dx I don't know how to...

Hello, I am asked to give the formal expression of the total number density of galaxies and explain why is this expression problematic in practice? From what I saw from my research and into my lectures, I have found the follwing relation which gives the number of galaxies ##N## with mass ##(m...

Homework Statement [/B] For reference: Book: Mathematical Statistics with Applications, 7th Ed., by Wackerly, Mendenhall, and Scheaffer. Problem: 10.81 From two normal populations with respective variances ##\sigma_1^2## and ##\sigma_2^2##, we observe independent sample variances ##S_1^2## and...

Homework Statement A DC current is flowing between two electrodes through a iron disk medium. Positive is attached to the copper shaft of the disc and the negative is attached to the outer brass periphery of the disk. The radius of the disk is 2,54mm (1 inch) and the height of the disk is 1cm...

Hello What is the meaning of the average velocity of gas molecules calculated by Boltzmann distribution (in kinetic theory of gases)? Does all molecules have the same average velocity?

Homework Statement "Let ##X,Y## be independent r.v.'s (EDITED) normally distributed with ##\mu=0,\sigma^2=1##. Find the distribution of ##W=2X-Y##. Homework Equations "If ##X,Y## are independent, then if ##Z=X+Y##, ##f_{Z}=\int_{\mathbb{R}} f_X(x)f_Y(z-x)\, dx##. The Attempt at a Solution...

Homework Statement (Scroll to bottom for the true question) Suppose we are to find the integral from -∞ to +∞ of (let’s just say) e-x2dx Homework Equations ∫∫f(x)g(y)dxdy = (∫f(x)dx)(∫g(y)dy) The Attempt at a Solution We can square the integral we want to solve for then use my relevant...

Write an expression for normal distribution for the data: Measured values are: 4,393; 4,372; 4,381; 4,373 and 4,401 thanks for help

Homework Statement "Show that if ##P(X=c)>0##, for some ##c\in \mathbb{R}##, then the distribution function ##F_X(x)=P(X\leq x)## is discontinuous at ##c##. Is the converse true?" Homework Equations Continuity of a distribution function: ##\lim_{\epsilon \rightarrow 0}F_X(x+\epsilon)=F_X(x)##...

Hello! Thanks for your time reading my questions. When I was studying quantum statistical mechanics, I get so confused about the relations between Pauli's exclusion principle and the Fermi-Dirac distributions. 1. The Pauli's exclusion principle says that: Two fermions can't occupy the same...

Homework Statement Long and thin sample of silicon is stationary illuminated with an intensive optical source which can be described by a generation function ##G(x)=\sum_{m=-\infty}^\infty Kδ(x-ma)## (Dirac comb function). Setting is room temperature and ##L_p## and ##D_p## are given. Find the...

Homework Statement I need help on solving this exercise : We have a ring of radius = ##a## uniformly charged (total charge = ##Q##) and on its axis a segment ##OA## (length = ##a## also) of uniformly distributed positive electric charges with the charge density ##\lambda'## and of total charge...

Hi, the trace of the extrinsic tensor K(Myu,Nu) in Alcubierre metric, relative to the foliation normal vector is non zero on the front x=rs+R and rear x=rs-R "walls". This is the normal volume component Tr =k(1,1)+k(2,2)+k(3,3) and should affect the Ricci tensor in Lorentzian/Minkowsky 4D. How...

Homework Statement Let X1, X2, ..., Xn be iid random variables with continuous CDF FX and suppose the common mean is E(Xi) = μ. Define random variables Y1, Y2, ..., Yn by Yi = 1 if Xi > μ; 0 if Xi ≤ μ. Find the distribution of ∑ni=1Yi. I'm having a hard time figuring out how to begin to find...

Hey guys, I've got this problem I've been trying to solve, but it makes little sense to me. I've tried a few things, but I feel like with each method, I've made no progress, and I haven't been able to make the problem make any more sense to me by trying those things. Here's the question: The...

Homework Statement This problem is belonging to a book, which is material for Vietnamese students who will take part in IPhO (International Physics Olympiad). Since this problem is written in Vietnamese, I will try my best to translate it to English: A vacuum diode consists of two parallel...

https://www.nikhef.nl/~h73/kn1c/praktikum/phywe/LEP/Experim/3_2_03.pdf In direction lab. I wonder why frequency of oscillator set at 50 s^(-1) ? I want to know if the frequency affects the speed of paricles?

Homework Statement Random variable Y has a binomial distribution with n trials and success probability X, where n is a given constant and X is a random variable with uniform (0,1) distribution. What is Var[Y]? Homework Equations E[Y] = np Var(Y) = np(1-p) for variance of a binomial...

Homework Statement Homework Equations dV= integral(kdQ/dR) The Attempt at a Solution So, I'm familiar with these type of problems but in 2D (like a line of uniform charge). When the y,z component is added, I'm kinda lost. i know dQ = p*dV= p*dx*dy*dz. (atleast i think it is). also the dR =...

Homework Statement A random variable Y has a binomial distribution with n trials and success probability X, where n is a given constant and X is a uniform(0,1) random variable. What is E[Y]? Homework Equations E[Y] = np The Attempt at a Solution The key is determining the probability of...

<Moderator's note: Moved from a technical forum and thus no template.> So, I have this problem and I am stuck on a sum. The problem I was given is the following: The probability of a given number n of events (0 ≤ n < ∞) in a counting experiment per time (e.g. radioactive decay events per...

Suppose ##X## ~ N(##\mu##,##\sigma^2##). Then ##\bar{X}## ~ N(##\mu##,##\frac{\sigma^2}{n}##), where ##\bar{X}## is the random variable for sample mean for samples of size ##n##. But when the population variance ##\sigma^2## is unknown and the sample size ##n## is small, ##\bar{X}## no longer...

Homework Statement Working through Purcell (among others) as fun applied math/math modeling refresher. But, I have struggled all week in establishing from first principles that the potential/field/distribution for a configuration of two capacitive disks of radius 1 and separation s along the...

Hello all, I have a Radial Distribution Function in which the y-axis ie., g(r) value goes up to 40. But the other atoms values for g(r) are, say within 5. So when i plot these two it is difficult to see the smaller graph. So how do i normalize these value..?? I have attached an image. Any...

Homework Statement I need to find the distribution coefficients for acetic acid of various concentrations in a ether/water system, but I'm not too sure of my calculations Homework Equations To get the concentrations of acetic acid in the aqueous phase I took the ([average concentration of...

Hi guys, For my (master) project I am trying to find the probability that a random variable, which is normally distributed, exceeds a quantile that is estimated by a limited number of observations. See attached for my attempt. - Is it correct? - How to incorporate the fact that the mean and...

Homework Statement Two thin conducting spherical shells have radii R1 and R2.Outer shell is charged to q and inner shell earthed.Find charge appearing on both the shells. Homework Equations The Attempt at a Solution Isnt the charge on inner shell 0 and charge on outer shell remains Q as it...

Hello. I am trying to decipher the formula, making sure I understand what exactly is going on in each part of the expression. I will be grateful for your guidance, corrections and help. Below I show the formula and the example for only 3 possible outcomes (in general it would be k) \(p =...

Homework Statement [/B] ##-1\leq\alpha\leq 1## ##f(y_1,y_2)=[1-\alpha\{(1-2e^{-y_1})(1-2e^{-y_2})\}]e^{-y_1-y_2}, 0\leq y_1, 0\leq y_2## and ##0## otherwise. Find ##V(Y_1-Y_2)##. Within what limits would you expect ##Y_1-Y_2## to fall? Homework Equations N/A The Attempt at a Solution...

Homework Statement For the RDF, we take the square of the radial component multiplied by 4pi r2 (the surface area of a sphere) and this gives us the probability density of finding an electron r distance away. Whats the point in multiplying it by r2? Homework Equations RDF= r2[R(r)]2 The...

I suddenly have a problem with the famous Maxwell velocity distribution. The maximum of this bell-shaped curve is commonly interpreted as the most probable velocity for a particle (see for instance https://en.wikipedia.org/wiki/Maxwell%E2%80%93Boltzmann_distribution: "The most probable speed...