Distribution Definition and 1000 Threads

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...

Hello all. I saw this problem in a book. I tried solving it, and compared it to the suggested solution. Results don't match, and I think that I am correct. Could you please help me decide what the right answer is ? This is the question: When coin 1 is flipped, it lands on heads with...

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...

Problem: Consider two parallel and large sheets with a surface area . One has a charge and the other is uncharged. q | | | | | | | | | | What would be the electric fields on the three regions as divided by the sheets ? General solution to problems like as told...

Homework Statement Given X,Y,Z are 3 N(1,1) random variables, (1) Find E[ XY | Y + Z = 1] Homework EquationsThe Attempt at a Solution I'm honestly completely lost in statistics... I didn't quite grasp the intuitive aspect of expectation because my professor lives in the numbers side and...

please check the video at 5:33. how can we find the partial derivative w.r.t n1 n2 and on? isn't each state (n1, n2 and on) one discrete state not a continuous variable? is it because we can have multiple particles in the given energy state? However its a finite discrete number. as far as I...

I am having an issue with finding the entropy in my program. I was asked to the find the entropy of the distribution as a function of time but i do not know where to start with entropy. I understand entropy but putting it in my program is where I am stuck Here is my code: # -*- coding: utf-8...

So my understanding of the T distribution is that if you do not know the variance of a population you estimate the distribution of the mean with the T distribution. But I am not sure about this because if you know the variance of the population, law of large numbers shrinks the variance...

Why do people say that RVs that have the normal distribution has a constant variance. What does that mean constant variance.

hey i really need help with solving this question. 1. Homework Statement the problem is in one dimention x ( 2 plates with diffrent K joined together) for x=0 T=500 ( constat temp) 0<x<L - electric wire is generating heat that maintane the constant temp in x=0 ,it has K=40W/mK. L<x<2L - there...

Hello everyone, I am currently considering a set of random variables, \vec{x} = [x_1,x_2,...x_N] which are know to follow a multivariate normal distribution, P(\vec{x}) \propto \mathrm{exp}(-\frac{1}{2}(\vec{x}-\vec{\mu})^\mathrm{T}\Sigma^{-1}(\vec{x}-\vec{\mu})) The covariance matrix Σ and...

How do you know that if two random variables have the same moment generating function then they have the same probability distribution.

Homework Statement We assume that the number of structural flaws on a long wire have obey Poisson distribution law. On average we find 1 flaw every 5 meters. a) What is the probability that a 20 m long section will have maximum 2 flaws? b) We slice the wire into 1 m long sections. What is the...

http://ecee.colorado.edu/~bart/book/book/chapter2/pdf/ch2_5_5.pdfcan you please tell me where f/(f(gi,fi) is from? and also how to get to (2.5.13)

Is there a relatively simple algorithm to compute the area in percentage under the curve as represented by a sigma value? For example; 3 sigma = 99.7 2 sigma = 95 1 sigma = 68.3 Now suppose I wanted to know 2.5 sigma without a table.

Hello, I would like to calculate the current distribution in a coaxial cable where the skin effect is significant. I asked this question on stackexchange and I provided pictures and more details there...

Any help would be much appreciated. The problem lies in the non-Gaussian distribution of the sample. If we take the entire data set of total fish catch, the skewness statistic equals 7.463 with a std. error of skewness of 0.39. Accordingly, the Z dist. (7.463/0.39)=19.14. Overall, the...

Homework Statement given set C = {(x,y)|x,y are integers, x^2 + |y| <= 2} Suppose they are uniformly distributed and we pick a point completely at random, thus p(x,y)= 1/11 Homework Equations Listing it all out, R(X) = {-1,-2,0,1,2} = R(y) The Attempt at a Solution My problem is that when I...

Homework Statement suppose that 50 random samples of size n = 10 are to be taken from a population having the discrete uniform distribution f(x) = 1/10 for x = 0,1,2,...,9 0 elsewhere sampling is with replacement so that we are sampling from an infinite population. we get 50 random...

I have a question about photons and the Schrödinger equation. Photons behave like particles but also as waves. I understand that this can be described by the Schrödinger equation as a photon having a certain probability to be somewhere. If I understand this correctly, I take it that there are...

Hey all, I just wanted confirmation. The thermal energy distribution of molecules in a system corresponds directly to its blackbody curve right?

Homework Statement A triangle is given with the points: Q1 = +2.0 x 10-5 C 2.0 m from Q3 = -3.0 x 10-5 C AND Q1 = +2.0 x 10-5 C 2.0 m from Q2 = -3.0 x 10-5 CThe triangle is a right triangle, with Q1 at the 90 degree angle.FIND THE NET FORCE OF CHARGE 1Homework Equations [/B] FE21 = FE31...

The assignment was already turned in a while ago, but I am currently reviewing all the past homework and trying to resolve the problems I couldn't understand. The website software gives the correct multiple choice or numerical answer, but not the steps. They gave me a weird answer and I didn't...

Suppose the hydrogen atom consists of a positive point charge (+e), located in the center of the atom, which is surrounded by a negative charge (-e), distributed in the space around it. The space distribution of the negative charge changes according to the law p=Ce^(−2r/R), where C is a...

Homework Statement It is known that the IQ score of ten-year-old children in a particular population has a normal distribution with mean 100 and standard deviation 15. (a) What proportion of this population have an IQ score above 115? (b) Mary’s IQ is equal to the 80th percentile of this...

Homework Statement 4. Let X and Y have the joint probability distribution (a) Find P(X +Y ≤ 4). (b) Find the marginal probability distributions f1(x) and f2(y). (c) Find P(X < 2|Y = 2). (d) Are X and Y independent? The Attempt at a Solution a) f(1,1) + f(1,2) + f(1,3) + f(2,1) + f(2,2) +...

Homework Statement A telephone operator receives four phone calls in three minutes on the average. Let a Poisson random number X denote the number of phone calls per minute to this operator. (a) Find the probability that this operator receives two phone calls in a minute. (b) Find the...

Homework Statement 1. A fair coin is tossed 100 times. (a) Find an approximate probability of getting at least 60 heads. (b) Find an approximate probability of getting exactly 60 heads. The Attempt at a Solution part b) would be b(60;100,.5) part a) we would need the table for the cumulative...

Homework Statement A teacher has an infinite flow of papers to mark. They appear in his office at random times, at an average rate of 10 a day. On average 10% of the manuscripts are free from errors. What is the probability that the teacher will see exactly one error-free manuscript (a) after...

A manufacturer has designed a process to produce pipes that are 10 feet long. The distribution of the pipe length, however, is actually Uniform on the interval 10 feet to 10.57 feet. Assume that the lengths of individual pipes produced by the process are independent. Let X and Y represent the...

Homework Statement A nonconducting sphere 1.3 m in diameter with its center on the x axis at x = 4 m carries a uniform volume charge of density ρ = 4.8 µC/m3. Surrounding the sphere is a spherical shell with a diameter of 2.6 m and a uniform surface charge density σ = -1.2 µC/m2. Calculate the...