Distribution Definition and 1000 Threads

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...

X,Y r.v statistically independent ,with exponential Distribution. calculate the density function of X/Y (Let $X$ have distribution ${\lambda}e^{-{\lambda}x}$ and $Y$ have distribution ${\lambda}e^{-{\lambda}y}$ i know i should use transformtion u=X+Y ;v=X/Y to solve it)

Hi. This may be a trivial question, but I'm unable to find a definitve answer. How is the mass on a atomic nucleus distributed? I read somewhere that it was uniformly distributed, and somewhere else that it resembled a normal distribution. Can you help me out? Thank you.

Homework Statement Question: Find the number of trials needed to be 90% sure of at least three or more success, given that probability of one success is 0.2 Homework Equations N/A The Attempt at a Solution My initial attempt at the problem was finding the probability of at least...

What is the probable cause of overvoltage in three phase secondary distribution line? Is it Possible to have an unbalance voltage in secondary distribution line? How do we solve this? Situation: 1-disconnecting switch of a three phase transformer bank has been open in Primary distribution line...

The average if the binomial distribution with probability k for succes is simply: <> = Nk So this means that if <> = 1 the distribution function must be peaked around 1. In general when is it a good approximation (i.e. when is the function peaked sufficiently narrow) to say that the...

Suppose I have 6 die and toss them. The probability to have n 6's is binomially distributed with parameter 1/6. Now suppose instead tossing the 6 die and having 1/6 probability for a 6 each dice's probability to show 6 grows continously in the time interval t=0 to t from 0 to 1/6. Can I then...

Hello everybody. This is my first post here and I hope I'm not asking a question that's been addressed already (I did try to use the search function, but couldn't find what I'm looking for). Both the Bayes theorem and the law of large numbers are mathematical theorems derived from...

good day everyone, I wonder if anyone can direct me please on the international standard number or name that explain the safety and standard procedures in better distribution of power in breakers and panels from transformers. in short, as I learned in my school and as best practice that...

As a high schooler, what I can deduce from Planck's distribution's bell shape is that the majority of the atoms of a body above 0k possesses a certain K.E which is the average K.E which leads to the presence of a peak point in the distribution. While the minority posses higher or lower K.E...

Is there a relation between these two distributions ?

The number of hours, N, of daylight at a certain location can be expressed as N(d)=12+6sin(2πd/365) where d=day of the year starting with March 21. (a) What is the probability distribution function for hours of daylight if you assume the day of the year is a random variable? (b) What is the...

A system has two non-degenerate energy levels E1 and E2, where E2>E1>0. The system is at tempreture T. The Average energy of the system is = E1+E2e^(-B*deltaE) / 1+e^(-B*deltaE) where deltaE= E2 -E1 and B=1/kT (k=Boltzmann constant). show that for very low temperatures kT<<deltaE, average...

Homework Statement Generate 100 data points from a continuous uniform distribution with mean = 10 and variance = 4 Homework Equations u = (a+b)/2 var = (b-a)^2 / 12 r = a + (b-a).*rand(100,1); The Attempt at a Solution points = 100 m1 = 10 v1 = 4 syms a b [a...

In the book 'Macroscopic and Statistical Thermodynamics' they derived the Maxwell-Boltzmann distribution by maximizing entropy using lagrangian multipliers with constants ##\alpha## and ##\beta##. The final result is given as: \frac{\overline {n_j}}{g_j} = e^{-\beta \epsilon_j}e^{-\alpha}...

A certain particle is interacting with a reservoir at 500 k and can be in any four possible states. The ground state has energy 3.1 eV and three excited states all have the same energy. what is the probability that the particle is in ground state? what is the probability that the particle is in...

what is breit wigner distribution function ? it is used in resonance scan means it decides the no of events for any specific channel. i am also giving the link of the paper where i found this http://pos.sissa.it/archive/conferences/160/018/Bormio2012_018.pdf please help me out thank you

Homework Statement In fact, there are two problems, and I want to know whether my solutions are right or not. 1- Two charged line with density of 15 n c/m along the x and y axes (x\pm\infty, y\pm\infty), Find the Electric field at: (a) (0,0,4) (b) (0,5,4). 2- A cylinder with radius \rho=8cm...

It seems to me that if we consider different methods of generating a distribution of an infinite number of samples of and unbounded real number then we get some distinct results. 1) If we randomly sample a value, then its probability must be non-zero, which is also true of any other value...

Distributions: sample mean and variance, and variance of sample means? Hi. Say you have a population, and from there you can draw a stochastic variable ##X## with a specified distribution. So you take out a few sizeable samples from the population, and calculate the mean and variance of ##X##...

Is the charge distribution of an electron uniform, or is there more charge concentrated near the center or perimeter?

Greetings all, This is my first post, and I preface by saying I attempted to search for a solution before posting. Accept my apologies if this topic has been covered in some way; I'll gladly move/repost. Anyhow, here is the situation: I am a teacher and my students are aged 9 - 12 (Mixed...

I'm looking primarily for answers from people who have been on admission committees or have otherwise reviewed applications from undergraduate students. When you look at a student's transcript, is the distribution of his/her grades a factor at all? For example, I performed only around average...

Hello, I have a problem. I have two independent variables, X and Y. I use polar coordinates so X=r*cos(fi) and Y=r*sin(fi) R >= 0 and -pi <= fi <= pi I got two distributions: for R is: r*e^((-r^2)/2) and for fi: 1/2pi but now I don't know which kind of distribution is for each of them (I...

Homework Statement The data contains 2500 integers, each is either a 0, 1 or 2: zeroes: 1240 ones: 1014 two's: 246 Does the data follow Poisson, geometric, binomial or negative-binomial distribution? Homework Equations The Attempt at a Solution The mean of the data is...

Hi, does anyone know how much of the universes's iron or carbon has been made in supernovae that formed black holes? Is it 5, 10, 50 % of the iron currently pressent here? And, if se, do we have any idea how much of the average stars content gets traped in the BH versus the mass of the...

A certain couple is equally likely to have either a boy or a girl. If the family has four children, let X denote the number of girls. Determine the probability distribution of X. (Hint: There are 16 possible equally likely outcomes. One is GBBB, meaning the first born is a girl and the next...

In quantum mechanics, there doesn't seem to be a joint distribution of position and momentum. But in Bohmian mechanics there is. But Bohmian mechanics is quantum mechanics, so what is the error in my reasoning?

Homework Statement Hey Guys! Here's my problem: ψ=2(Z/a)^3/2*e^ρ/2 for the 1s orbital of a hydrogen atom. Write down the radial distribution function expression (P) of a 1s electron and determine the most likely radius. ρ=2Zr/a Z nuclear charge r radius a Bohr's radius Homework...

Homework Statement Let X1,X2,X3 be a random sample from a normal distribution with mean μ≠0 and variance σ2=1/24. What are the values of a and b, respectively, in order for L=aX1+4X2+bX3 to have standard normal distribution?Homework Equations σ=1/√24 Converting normal distribution to...

A boy is playing with a biased coin. The probabilty of obtaining a head with the coin is 0.4. Determine the probability that the boy will require at least eleven tosses before obtaining his third head. I have been trying but can't get it at all... Can someone please explain me how to solve...

Homework Statement If random variables X and Y are independent and both belong to Possion distribution of parameters \lambda_1 and \lambda_2 , then what is the conditional distribution of X when the condition X + Y = m is given? Homework Equations Possion distribution of...

Greetings everyone. I do not have an extensive background in Power. I've recently been brushing up on topics from undergrad related to power distribution and residential wiring in general. I understand that in general, houses in the US are fed a three wire, split-phase 240V power from the...

If $$( X,Y )$$ has the normal distributions in two dimensions with zero means and unit variances and the correlation coefficient $$ r$$, then how to prove that the expectation of the greater of $$X$$ and $$Y$$ is $$\sqrt{(1-r)\pi}$$?

I have found that: For l = 1: \sum_{m=-l}^l |Y_l^m|^2 = \frac{3}{4\pi} For l = 2: \sum_{m=-l}^l |Y_l^m|^2 = \frac{5}{4\pi} What significance does this have for the probability distribution in an hydrogen atom?