Distribution Definition and 1000 Threads

Homework Statement My source textbook is the community college / junior college (confer: undergraduate-lower division) probability and statistics textbook: An Introduction to Mathematical Statistics and Its Applications, 2nd Edition Authors: Richard J. Larsen, Morris L. Marx 1986...

Hello, I'm trying to write a monte carlo simulation for an optical analysis. Half the area of a sphere is within 60 degrees of the poles. Hence, I'm assuming half of randomly directed radiation should fall within 60 degrees of the poles, when radiation is generated at the center of the...

I am studying an article which involves stochastic variables http://www.rmki.kfki.hu/~diosi/prints/1985pla112p288.pdf. The author defines a probability distribution of a stochastic potential V by a generator functional G[h] = \left<exp\left(i\int...

I am currently reading "Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles" by Robert Eisberg and Robert Resnick (2nd edition). In Appendix C they derive the boltzman distribution and they seem to be saying something that seems to me to be patently false. If you have the book...

Homework Statement The Binomial Distribution - already developed by Jacob Bernoulli (in 1713), et alii, before Abraham de Moivre (1667-1754 CE), et alii, developed the Normal Distribution as an approximation for it (id est, the Binomial Distribution) - gives the discrete probability...

The name in the title is probably not what it's called but it so similar that I chose it anyways. This is a problem I've been looking into on my spare time and I'm having a difficult time nailing it down. Essentially, it's an "extension" of the negative binomial distribution in the sense that...

Homework Statement I have a question that looks so stupid that I have never dared to ask. If I want to measure the time average from t=0s to t=1s of a given f(t), the solution is compute the following integral: TA = 1/T*∫F(t)dt However, I have some doubts about this calculus.Homework...

I have a set of scored items with the scores in the interval [0,1]. Roughly speaking the distribution of scores is about 50% equal to 0 and then sloping steeply downward all the way toward one or near to one. I want to fit this data to a distribution and use that down the road in some...

In my country, the Electrical distribution box has two sections lighting section 300 mA and power section 30 mA why the lighting section taking more current than the power ?? Shouldn't the power take more ??

Hi guys I got a question on the poisson distribution and never previously done stats at all. It follows: The mean count of a radioactive substance is 25 disintegrations per minute. Using the Poisson distribution, find the probability that, in a time of 12 seconds, there are- i) No...

Homework Statement I have to find the Boltzmann ditribution of a 1 dimensional ideal gas. The answer is given as: \frac{dn}{n}=\sqrt{\frac{m}{2piKT}}e^{(\frac{-mc^2}{2KT})} For the second part I have to find the mean kinetic energy. 2. Homework Equations / Attempt For part 1...

Homework Statement my question is on part ii , can someone suggest how to do part ii please? thanks.. by the way , i have attached the working for part i Homework Equations The Attempt at a Solution

I don't know how to integrate the Maxwell-Boltzmann distribution without approximation or help from Maple. Given the Maxwell-Boltzmann distribution: f(v) = 4\pi\left[\frac{m}{2\pi kT}\right]^{3/2}v^2\textrm{exp}\left[\frac{-mv^2}{2kT}\right] Observe the appearance of the Boltzmann factor...

I have what I think is probably a basic question from probability and statistics (about which I'm pretty ignorant). If I have a set of projectile trajectories that were generated by a Monte Carlo process, and I'd like to know the probability the projectile will come within distance d of some...

As I understand it, one result of the central limit theorem is that the sampling distribution of means drawn from any population will be approximately normal. Assume the population consist of Bernoulli trials with a given probability p and we want to estimate p. Then our population consist of...

I don't know how to integrate the Maxwell-Boltzmann distribution without approximation or help from Maple. Given the Maxwell-Boltzmann distribution: f(v) = 4*pi*[m/(2*pi*k*T)]^(3/2)*v^2*exp[(-m*v^2)/(2*k*T)] Observe the appearance of the Boltzmann factor exp[(-m*v^2)/(2*k*T)] with E =...

Homework Statement http://postimg.org/image/bleosmrep/ Homework Equations The Attempt at a Solution can someone explain the last line of the solution; where did 1 - 6.25/10^2 come from?

Help? Suppose the random variable Y has an EXP(2) distribution. What is P(Y > 1)? (Round to four decimal places as appropriate.)

please refer to the second line of solution, since we only concerned about the probability of getting number (5) , then why can't I just just say P=(5/6)^5 , why should I times =(5/6)^5 with (1/6)^2 ?

For two-body decay, in the center of mass frame, final particle distribution is, $$ W^*(\cos\theta^*,\phi^*) = \frac{1}{4\pi}(1+\alpha\cos\theta^*) $$ We have the normalization relation , ##\int W^*(\cos\theta^*,\phi^*)d\cos\theta^* d\phi^*=1##. And we also know that in CM frame ##p^*##...

For my research on astrophysics for the summer, a professor gave me this assignment but I don't know where to start. The question is: What methods could be used to find the dark matter distribution around a galaxy's central black hole?

So, I've got a charge distribution given by: \begin{equation} \rho(r,\phi,z)=\frac{q}{2\pi R}\delta(r-R)\delta(z)\cos(2\phi) \end{equation} This, if I'm not mistaken, translates into a circular charge distribution located in the z-plane, a distance R from origo. Thus \begin{equation}...

Hi! Suppose we have two variables Y and Z that depend on a third one, X. We are given P(x), P(y|x) and P(z|x). The joint probability distribution P(x,y,z), according to the chain probability rule, is given by P(x,y,z) = P(x)P(y|x)P(z|x,y) But how can we compute P(z|x,y) with the given...

Hi. I notice that some values of X on the exponential distribution PDF have a value of around 1. I understand the integral ends up being one, since those values of X are less than 1. But P(X) at those points still gets to 1, or thereabouts. How does that make sense, that the probability of a...

What is the significance of the standard deviation (equal to the mean) in an exponential distribution? For example, as compared to the standard deviation in the normal distribution, which conforms to the '68-95-99.7' rule? thanks

Homework Statement I am a freshman in physics, just done a lab about radioactive decay. I've measured the # of beta particles per second 400 times and got the frequency of each number K using Excel. I'm supposed to take the data and fit it to a puason distribution in MATlab. The data points...

I have a formula to get an average time that an average user spends reading a web page before going to the next one, that takes as input the number of words on the page. I want to use this in conjunction with a probability distribution to try to accurately model an 'average user' that is not...

Base on maxwell-boltzmann distribution,we can calculate the average velocity of gas molecule . i read a book and it proves like that average velocity=\int vf(v) dv I don't understand why we don't have to divide it by N because we should be calculating the average,but not the total. Would...

I have ##\bar{X}## ~ ##N(\mu , 9/25)## I have ##E[X] = \mu## ##Var[X] = 9/25## ##SD[X] = 3/5 = 0.6## An interval for ##\bar{X}## has been recorded: ##\bar{X} \pm 1.05##. I asked to find ##P(\bar{X} > \mu + 1.05)## I can "normalize" the distribution through: ##Z =...

Suppose I have an box (set) containing two different colored balls, red and blue, say. Now, suppose the balls differ in size, where the size of the red balls has one particular distribution and those of the blue another. How can we describe the distribution of the balls in the box?

This is a vague question and I apologize in advance for not being able to explain it better. I'm combining r.v.'s from different populations (distributions). The resulting population can be thought to come from a mixture distribution. I think another way of describing the resulting...

Homework Statement A long, hollow, thick elastic cylinder (E , v) is surrounded by a thin elastic band of thickness t made of a different material (E_2 , v_2). The fit is ideal, such that neither a gap nor a pressure exists. An internal pressure p is then applied at the inside radius (r=a) of...

let X1 and X2 be independent Poisson variables with respective parameters μ1 and μ2. Let S = X1 + X2. Is X1 given S=s a binomial dsitribution? What is the parameters? I just can show that S is a Poisson with mean μ1 + μ2. But I am not confirm X1 given S is a binomial or not? Someone please...

Lets say I have 8 samples (weight) of 4 ingredients in particular food by X brand and another 8 samples by Y brand. I would like to test to see if there is any difference between the two brands in terms of weight of particular ingredients. However, I am not sure what statistic test to run and I...

Homework Statement The ground sate of a Hydrogen-like atom is given by the wavefunction: $$R_{10}(r)= 2\left(\frac{Z}{r_0}\right)^{3/2}e^{Zr/r_0}$$ and the Probability distribution is $$P(r)=4\pi r^2 |R_{10}|^2$$ At what distance is the most probable radius of the electron? Homework...

ok, so I have a list of students with GPA, I checked the probability plot and I think its a Exponential distribution, take a look: So I am given a χ-bar to prove, and I have to prove or test it with three different types of test, I don't know which ones or how to do them in miniTab...

Homework Statement "Cans of lemon juice are supposed to contain 440 ml of juice. It is found that the actual volume of juice in a can is normally distributed with mean 445 ml and standard deviation 3.6 ml." It is found that 94% of the cans contain between 445−c ml and 445+c ml of juice. (ii)...

How is dark matter distributed (as far as we know)? Let's stay with a single galaxy like the Milky Way. I heard that dark matter is even more concentrated in the center than in the halo, that it is falling off when moving outside, but since the halo is so huge (how huge, ten times larger?)...

Homework Statement Two independent series of experiments are performed. The probability of a positive result (independent of each other) in the respective series are given by p and q. Let X and Y be be the amount of experiments before the first negative result occur in the respective series...

Hi !, my problem is the following: Let $F_X (x)$ an distribution function strictly monotone for the random variable $X$ and it's defined the new random variable $Y=F_X (X).$ Find the cumulative distribution function of $Y$.

A problem i made up for some of my friends who need help with discrete distributions tables. Can you do it? Dice Generator Part I: 1. Construct a discrete probability distribution table for a fair six-sided dice. (Round according to example) 2. Calculate the mean, variance, and standard...

Hello, From an offset zener diode breakdown circuit, I have collected a set of bytes from an ADC. The values distribute normally as integers between 0 and 1024 with a mean of 512. I would like to use the data to create a set of random integers that distribute uniformly. So far, I have...

Homework Statement Homework Equations The Attempt at a Solution I DO NOT NEED HELP WRITING THE PROGRAM! I'm just trying to figure out the basics behind it. Since this is an integral I will be solving this problem by using riemann sums. Where I'm having the most trouble is in the...

What is the relationship between the Frequency Distribution, Cumulative Distribution and Particle Size?

Homework Statement A rectangular field is gridded into squares of side 1m. at one time of the year the number of snails in the field can be modeled by a Poisson distribution with mean 2.25 per m^2. (i) a random sample of 120 squares is observed and the number of snails in each square...

Homework Statement Suppose that particles of two different species, A and B, can be chosen with probability p_A and p_B, respectively. What would be the probability p(N_A;N) that N_A out of N particles are of type A? The Attempt at a Solution I figured this would correspond to a binomial...

Hello, it is well-known that the Chi-square test between an observed distribution O and an expected distribution E can be interpreted as a test based on (twice) the second order Taylor approximation of the Kullback-Leibler divergence, i.e.: 2\,\mathcal{D}_{KL}(O \| E) \approx \sum_i...

Consider two spherical hollow conductors, charged to Q1 and Q2 coulombs respectively. What happens when one is placed within the other, and they are connected by a thin metallic wire? I do know that if they were placed at a distance from each other, the charge is distributed in the ratio of the...

Homework Statement Let X1, X2,...,Xn be a random sample from the exponential distribution with mean θ and \overline{X} = \sum^{n}_{i = 1}X_i Show that \overline{X} ~ Gamma(n, \frac{n}{θ}) Homework Equations θ = \frac{1}{λ} MGF Exponential Distribution = \frac{λ}{λ - t} MGF Gamma...

Hi all, I have a couple questions about radiation from radioactive elements. I've read a lot of articles on the different types of radiation given off by elements undergoing nuclear decay (alpha, beta, and gamma) but I haven't been able to answer the following question: What is the...