Distribution Definition and 1000 Threads

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...

Hello, For this type of question: There are 5 green and 45 red marbles in the urn. Standing next to the urn, you close your eyes and draw 10 marbles without replacement. What is the probability that exactly 4 of the 10 are green? I understand that I can use Hypergeometric distribution, which...

Homework Statement 1. According to the Maxwell-Boltzman law of theoretical physics, the probability density of a gas molecule is ##f(v) = kv^2e^{-\beta v^2}## if ##v > 0## and ##f(v) = 0## otherwise, where ##\beta## depends on its mass and absolute temperature, and ##k## is an appropriate...

Homework Statement A multiple choice test consists of a series of questions, each with four possible answers. How many questions are needed in order to be 99% confident that a student who guesses blindly at each question scores no more than 35% on the test? Homework Equations So I know that...

Hi all, I refer to the following pdf document, in particular the appendix: http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1974A%26A...37..183A&link_type=ARTICLE&db_key=AST&high= End goal is to distribute N stars each having mass m (looks like equal mass stars is the easiest scenario)...

Homework Statement A gas has a hypothetical speed distribution for N gas molecules with N(v) = Cv^2 for 0 < v < V0. Find (i) an expression for C in terms of N and v0 (ii) the average speed of the particles Homework Equations N/A The Attempt at a Solution (i) integrating N(v) with respect to v...

Homework Statement \textbf{The Logarithmic Series Distribution}. We will examine the properties of a the Logarithmic Series Distribution. We will check that is is a probability function and compute a general term for factorial moments and, hence, compute its mean and variance. This distribution...

Homework Statement Homework Equations The Attempt at a Solution Im confused by this question, just looking at the diagram without any maths you can see what would happen. C and D would want to reach equilibrium and be at the same level so the pressure down on D would be the difference in...

Hi, what are the possible reasons for selecting 11kV underground distribution system vs 22kV underground distribution system for urban area. I know about 22kV can carry twice the load compared to 22kV. How about impacts of pricing, fault level, stepdown from 132 kv to 22/kv etc. Thanks

Homework Statement [/B] A company produces batches of 1800 axle shafts . These are tested to determine the proportion of those with too rough surface according to the standards set in the industry. The quality control department of a sample of 150 axle shafts in a lot and concluded that there...

Hi all, I saw some figures about potential (contour) plot in some articles that has some beautiful gradient lines. The shape is quite weird but you can see clearly there are some strong concentration of potential at some places. For example, if you have 300x300 grids, there shows strong...

Hi, i'm performing a simulation about this potential http://motion.cs.umn.edu/PowerLaw/ I calculated the radial distribution function succesfully but i don't know how these guys are normalized the other pair distribution function, as a function of time to collision. Could anyone help me? Thanks!

I'm watching a Stat. Mech. lecture and in it, the lecturer mentions a "general probability distribution" but doesn't explain what exactly that is, yet in the context of the video, everything necessary to understand is understood. On some cursory google searches I'm finding several hits for a...

Homework Statement We ask a person to taste 18 biscuits , 8 made to butter ( the other 10 are made to margarine ) , and to identify 8 butter cookies . He does not know the exact number of butter cookies . As he sees no difference , he randomly selects those he claims to be butter . Y = the...

Homework Statement A charge distribution has uniform density in the x-y directions and varies with z according to: ρ(z) = ρ0e−|z|/t where ρ0 and t are constants. (a) Find the potential V (z) and the electric field E(z) (b) Sketch them clearly showing their behaviors in the regions |z| ≪ t...

1. Does anyone know why for an isotropic distribution function, pressure tensor reduces to a scalar pressure? For instance, for a Maxwellian distribution P=A ∫ vx vy exp-(vx2 + vy2 + vz2) dvx dvy dvz is not zero. I think everybody should realize how bogus some of the authors are. Google...

Homework Statement Consider f = wT x, where p(w) ∼ N (w|0, Σ). Show that p(f|x) is Gaussian. The Attempt at a Solution [/B] So there are apparently two approaches to this problem using either the linearity of f in terms of w or moment generating functions. But I'm having a lot of trouble...

Homework Statement For my project I need to compute the average the number of photons given by the expression: ##\bar{n}= \frac{e^{-\bar{h}\omega/\kappa T}}{1-e^{-\bar{h} \omega / \kappa T}}## where ##\kappa## is the Boltzmann constant and ##\omega## is the oscillator frequency. For the...

Let's say my probability function is given by: p(y1,y2)=Γ(y1+y2+γ)/((y1+y2)!*Γ(γ)), when γ>0 is known. I suppose it is from an exponential family but I can't write in canonical form because I'm only familiar with exponential family with one variable so I'm confused now when there's to variable...

Homework Statement a) ∫δ( x² cos x) dx with x from -∞ to +∞ b) Integral over C, with C = unit circle ∫C δ(α-α0) a ds a =(1,1) Homework Equations a) δ(g(x)) =∑δ(x-xi)/|g'(xi)| b)? The Attempt at a Solution a) g(x) = x² cosx g'(x) = 2x cos x - x² sin x xi = 0 and (2n+1)π/2...

Hi Guys :) I have become interested in producing true random numbers of uniform distribution, and have come across this Numberphile video in my travels: The narration hints at the topic of converting numeric sequences of a curved distribution, inherently more likely to be closer to a mean...

Homework Statement Homework Equations ıt is nonhomog type ,2D heat conduction problem The Attempt at a Solution I don't understant To parts so I couldn't attemp a solution.

Please bare with me, this is my first post here (although I've read a lot on here over the past few months) Hopefully I've used the correct formatting etc. I've got to a sticking point on the final point of the question below (2iii) I'm pretty happy with my answers to 2i and 2ii so I've not...

Coulombs law states 2 point charges of opposite sign will attract where acting simultaneously on two point charges and as follows: The formula calculates the force that will act and implies the force be equally experienced by both points of charge even if one charge is much greater than...

Hello everyone, I'm stuck at a elementary stochastic problem. I have to calculate means, variance and co-variance for two random variables. Homework Statement Let r,g,b∈ℕ. r red, g green and b black balls are placed in an urn. The balls are then drawn one at a time with replacement, until a...

Homework Statement Hello, we were given homework, which is perfectly described by this picture. We should figure out F1 and F2 (it's number). I know that if the both angles are equal, it is easy to solve. However, now i should solve a situation when first angle (alpha) = 50 grades, the second...

Hello, Just looking into some clarrification. If a customer states that they want the following system, what is it they mean (note, it is 3-phase 4W 120/208V: 1200 A MAIN DISTRIBUTION C/W: 1- 600 A house panel feed 2 - 100 A tenant sections 2 - 200 A tenant sections Basically the 1200 A is...

Hello. I have a problem calculating the electric field from spherical charge distribution. The exercise is: 1. Homework Statement Homework Equations To solve the problem for $$ 0\le R < a$$ i tried 2 ways: $$ \vec{E} = \frac{\vec{a_R}}{4\pi\epsilon_0}\int_v\frac{1} {R^2}\rho dv $$ and the...

Hello all I have this question I am trying to solve. In an urn there are 6 balls, numbered: 1,2,3,4,5,6. We take 4 balls outs, without replacement. X - the minimal number we see Y - the maximal number we see I need to joint distribution. I understand that X is getting the values 1,2,3 while...

Hello all, I have this Poisson distribution question, which I find slightly tricky, and I'll explain why. The number of car accidents in a city has a Poisson distribution. In March the number was 150, in April 120, in May 110 and in June 120. Eight days are being chosen by random, not...

Homework Statement What is the most likely speed in Maxwell-Boltzamann distribution? Homework Equations f(v)dv=4\pi(\frac{m}{2 \pi kT})^{3/2}v^2Exp(-\frac{mv^2}{2kT})dv The Attempt at a Solution I know I need maximum of f(v) -> \frac{df}{dv}=0. But it is not trivial to do. I found some...

Homework Statement I am struggling with one of the end of chapter questions in my QM textbook (see attachment as I don't know how to show calculus on PF). It has thrown me because the chapter introduces some of the key principles in QM by talking about probability but then it randomly chucks in...

Homework Statement I am given a data set known to come from a poisson distribution. Homework Equations Poisson distribution The Attempt at a Solution I want to calculate the mean of the data set for use in the Poisson Distribution function. How do I best estimate this. Do I take the...

I have been studying a processing time for an industrial process. The present analysis just consists of finding the mean value as if the time was distributed normally. I took a sample of data and made a histogram of the data and realized it is not normally distributed at all. The normal...

Consider a scenario where samples are randomly selected with replacement. Suppose that the population has a probability distribution with mean µ and variance σ 2 . Each sample Xi , i = 1, 2, . . . , n will then have the same probability distribution with mean µ and variance σ 2 . Now, let us...

Homework Statement Compute the joint cumulative distribution function $F_XY(x,y)$? Homework Equations The marginal distribution function $F_X(x)$ \begin{equation} F_X(x)=P(X\leq x)= \begin{cases} 0,x<0\\ 0.6,0\leq x<1\\ 1,x\geq 1 \end{cases} \end{equation} and $F_Y(y)$ \begin{equation} F_Y=...

Homework Statement Homework Equations I know that ##F_g=(G*m_e*m)/r^2)## ##dr⃗ =drr_1+rdθθ_1.## ##F⃗ g⋅dr⃗ =−(Gm_em/r^2)*r_1⋅(drr_1+rdθθ_1)## ##F⃗ g⋅dr⃗ =−(Gm_em/r^2)(drr_1⋅r_1+r*dr*dθ*θ_1⋅r_1)## The Attempt at a Solution [/B] I don't understand why there is a dr in the 2nd term in the...

I am trying to make a FBD for equipment which is half out of the beam, I realize I can represent it with a single line of force. But how if I want to go for distribute load? which one is the correct one. (purposely not drawing reaction force on floor.)...

Fermi-Dirac distribution function is given by f(E)=(1)/(Aexp{E/k_{B}T}+1) here A is the normalization constant? How we can get A? E is the energy, k_{B} is the Boltzmann constant and T is the temperature. thank you

Hi, On Wikipedia (here), we can find that in following channels of nuclear fusion reactions: H-2 + H-3 -> He-4 (3.5 MeV) + n (14.1 Mev) H-2 + H-2 -> H-3 (1.01 MeV) + H-1 (3.02 MeV) H-2 + H-2 -> He-3 (0.82 MeV) + n (2.45 MeV) H-2 + He-3 -> He-4 (3.6 MeV) + H-1 (14.7 MeV) The released energy is...

So I new to probability and need someone to help me out if you could. I wanted to look into the probability of a process being complete if each operation of the process has its own likely hood of success or failure. I know that I should be using a binomial distribution to study the process...

Hi, I was wondering if two matrices with the same eigenvalues share the same PDF. Any ideas and/or references would be helpful. Thanks in advance

How to find the normalization constant of Fermi-Dirac distribution function.

Homework Statement Let X∼Geometric(p). Using Markov's inequality find an upper bound for P(X≥a), for a positive integer a. Compare the upper bound with the real value of P(X≥a). Then, using Chebyshev's inequality, find an upper bound for P(|X - EX| ≥ b). Homework Equations P(X≥a) ≤ Ex / a...

I don't understand charge distribution properly. Here is what I found somewhere Figure (1)shows three concentric thin spherical shells A,B and C of radii a,b and c respectively.The shells A and C are given charges q and -q respectively and the shell B is earthed.Find the charge appearing on the...

Homework Statement The joint probability density function of X and Y is given by f(x,y)=(6/7)(x^2+ xy/2) , 0<x<1, 0<y<2. (a) Find the pdf of X. (b) Find the cdf of X. (c) FindP(X<.5). (d) Determine the conditional pdf of Y given X = x. The Attempt at a Solution a) the pdf is what is...

The meters used in measurement have some level of accuracy. There is a probability distribution of measuring the true value, and that distribution curve for the accuracy of the meter has some standard deviation. And the component being measured also has it's own manufacturing distribution that...

I want to calculate the distribution function for the relative velocity v_r = v_1 - v_2 of two particles. Each particle velocity follows the Maxwell distribution for velocities. They have the same mass and temperature. Can I just multiplicate the Maxwell distributions of the two particles (and...

Homework Statement Derive the bernoulli binomial distribution by generalizing the probability of a coin flip. ## P(k, n) = \binom{n}{k}p^{k}q^{(n-k)} ##, q = p - 1 Homework Equations Combination: ## \binom{n}{k} = \frac {n!} {k!(n-k)!} ## Prob. of coin flip: ## \frac {\binom{n}{k}} {2^n}...

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...