Distribution Definition and 1000 Threads

Homework Statement The temperature distribution of a circ plate with radius ##a##, ##f(r,\theta,t)##, follows the diffusion equation ##\nabla^2f=\frac{1}{\alpha^2}\frac{\partial f}{\partial t}##, with a temperature of zero along the border. The initial temperature is...

Hi, so my question is along the lines of the following: If I'm looking at the decay channel H=>ZZ=>4 Muons, why would the resultant distribution for the mass of the parent Higgs be a Gaussian? Is it a case of the peak is the actual value of the Higgs at rest; those of greater mass are Higgs...

Hi Assume an x-coordinate from the unit circle is picked from a uniform distribution. This is the outcome of the random variable X with probability density function Xden(x) = 0.5 (-1 < x < 1). The random variable Y is related to the random variable X by Y = f(X) = √(1-X2) and X = g(Y) =...

Imagine an uncharged solid spherical conductor. Inside this spherical conductor, there is a cavity of a weird shape carved out of it. And somewhere inside this cavity, there is a charge +q (or rather, a charge distribution of total charge +q). The charge +q induces an opposite charge -q on the...

It's hard to type this out as there is a diagram and notation I can't find on the key board so I've attached an image of the question and answer. I've explained my solution below however I've also attached an image if it's too confusing with the lack of symbols! Problem involves uniform...

Homework Statement Due to the pollution from the industry around an apple farm, the apples grown there may be contaminated by heavy metals. It is believed that the amount of heavy metals in an apple of the farm follows the Normal distribution. N(16,16) which has a mean μ = 16 units and σ = √16...

I'm looking to model a system in which events are nearly perfectly randomly distributed but with a slight tendency for events to avoid each other. As you know, if the system were perfectly random, I could use a Poisson distribution. The probability distribution for the number of events would...

Homework Statement Automobile accidents occur in the United States over a 72 hour holiday period like events in a Poisson process with parameter lambda=10/hr. V is the time until the 10th accident a) what is expected value of V or E[V] and standard deviation? b) What is the probability that V...

in 11kv /230 v delta /star connected distribution transformer neutral not connected to earh,then if we touch the one phase (ex:R phase)of secondery line, shall we get shock or not?

Does anyone know the proof of joint moment generating functions for bivariate normal distributions? M_x,y (s,t)= E(e^(xs+yt))

Hi, so this is the example I have: Suppose that A, B, C are independent random variables, each being uniformly distributed over (0,1). (a) What is the joint cumulative distribution function of A, B, C? (b) What is the probability that all of the roots of the equation Ax^2 + Bx +C=0 are real...

While I do understand the story of the hypergeometric distribution, I was wondering if there's anything "geometric" about it, or if there's any connection between the distribution and "geometry". Can anyone throw some light on it? Thanks, Madhav

Hi all, The probability that a state is occupied means : 1) Fully Occupied by 2 electrons Spin up and Spin down or 2) Occupied by 1 electron only . Thanks

Dear all, I'm not a mathematician so please excuse me for a certain lack of strictness ... I work on random signals in physics, these signals are most of the time called "noise" for us. For example, we can speak about x(t), a time domain random signal. Very usually, the statistics...

In some books the radial distribution function is defined as 4pi*r^2*R(r)^2 and in others as r^2*R(r)^2. Thus, a factor of 4pi is differing. Which expression is correct and why?

i want to know the behavior of voltage in 11 KV underground and OH distribution line at different load conditions i.e. no load-full load ...

Homework Statement Four players play a board game which requires them to take it in turns to throw two fair dice. Each player throws the two dice once in each round. When a double is thrown the player moves forward six squares. Otherwise the player moves forward one square Homework Equations...

Hi, can anyone please guide me how to draw the distribution curves for radial wave function of an orbital? Please explain stepwise and in easy way. Thanks.

Homework Statement http://imgur.com/EiCFIDe Homework Equations E = kq/r2 λ = dq/dx Q = λa The Attempt at a Solution Here is the book solution: http://imgur.com/aKSeKo0 I need help with part (a). I understand everything in the solution except for the distance they used for between (r2 in...

It is a cylindrical ac machine. If we want to produce a sinusoidal voltage, we need B (magnetic density) to vary sinusoidally. To get B vary sinusoidally, we need to get H(magnetic intensity) to vary sinusoidally. To get H vary sinusoidal, the best way is to vary the numbers in the air gap...

Homework Statement The technical specification of a particular electrical product states that the probability of its failure with time is given by the function: f(t) = 1 - ke^(-t/t0) if 0 < t < tmax f(t) = 0 if t > tmax where t is the time of service...

Let $X$ = the time between two successive arrivals at the drive-up window of a local bank. $X$ has an exponential distribution with $\lambda = 2$. That is the probability density of $X$ is $f(X | \lambda) = \lambda e^{-\lambda x}, X > 0 $ with $\lambda = 2$. Compute the following: a) The...

I want to create an array of numbers between 0 and 0.1 where the points are clustered around an arbitrary point x1 (0 < x1 < 0.1). I want the points to get exponentially closer together near x1 from either side and and get further apart towards the outer limits. I am using MatLab and was trying...

Hi. I normally can solve poisson distribution questions with ease. But this one question had me thinking for hours on end with no solution. It would be great if someone can help me. QN: The number of incoming calls per minute, X, to a telephone exchange has a Poisson distribution with mean 2...

Problem: McBurger’s drive-thru has only one service window and serves an average of 2 customers every 5 minutes. 70% of customers order drinks from the drive-thru. The manager monitors the employee at the drive-thru for the next 3 hours. He will give the employee a raise if exactly 20 customers...

Hey all, So I have a small convergent nozzle that I'm modelling in Abaqus and I'm wondering how I could work out the pressure distribution so I can apply the correct load. The problem is I only know the pressure being fed to it by air compressor. Is there a way to use Bernoulli s or some other...

Could anyone explain in laymen terms what really the beta function does as said in Beta Function:https://en.wikipedia.org/wiki/Beta_function .I know that gamma function is used to find the factorial of real numbers but when it comes to beta function I can't get what really beta function does.I...

Homework Statement Suppose that diastolic blood pressures (DBPs) for men aged 35-44 are normally distributed with a mean of 80 (mm Hg) and a standard deviation of 10. What's the probability that in a random sample of 5 subjects, 4 or more have DBPs more than 90? Homework EquationsThe Attempt...

Homework Statement Customers arrive in single server queue to be serviced according to Poisson process with intensity 5 customers an hour. (a) If the customers begin to arrive at 8am, find the probability that at least 4 customers arrived between 9am and 10am. (b) Find the probability that the...

Hello, I am stuck at this exercise: 1. Homework Statement X ~ U(0, a), a > 0 and Y = min(X; a=2). - Find the cumulative distribution function of Y -Is the variable Y continuous ? Homework Equations 3. The Attempt at a Solution [/B] The density function for X is f(t)= 1/a if 0≤t≤a , 0...

Hi comunity! I need to make a code o a normal distribution of velocities, starting whit a random secuence uniformly distributed between [0,1]. I am using FNT95, with Plato. I want to obtain a ''for'' bucle with I=1,N for the velocities. It is importan for the distribution to have sigma defined...

Given: Assume that f (x) is continuous at x = 0 and vanishes as x→±∞. Hint. Replace x by y/n and take lim n→∞ before integrating. I apply the hint and get $ \frac{1}{\pi}\int_{-\infty}^{\infty} \,{\lim_{{n}\to{\infty}}}{\frac{sin y}{y}} \,dy $ For the limit, as n -> ${\infty}$ , y -> 0. By...

Hello! I encountered this simple model for drug distribution in a textbook, but was not able to come up with the solution myself. It's been bothering me way too much past two days... Perhaps more so because of the "Equation 7-1 is easily solved" part. Hints/help would be much appreciated...

dE = ke(dq/r2) How to change to complicated equation in the following picture?

Since most planets in the earliest stages of formation are very hot and fluid, why is it that we find on Earth areas where there are substantial deposits of heavier elements - gold, uranium, etc in the crust? Intuition suggests that these relatively rare elements would become widely dispersed...

Homework Statement P is the probability that a person aged x years will die in a year. Find the probability that out of 5 men A,B,C,D and E, each of x years, A will die in the year and be the first to die. Homework EquationsThe Attempt at a Solution I fixed A in the first place with...

Given five data points (minimum, 25th percentile, 50th percentile, 75th percentile, maximum), do I have enough information to be able to construct what a normal (Gaussian) distribution would look like? I have no data on any other statistical information (population size, mean, median, mode...

Homework Statement Find P(X>130) where P(X > 130) = 1 − Φ( (130 − µ)/σ ) Homework Equations Φ is the normal distribution density function: http://en.wikipedia.org/wiki/Normal_distribution The Attempt at a Solution This is pretty simple to use in R if one knew how to. I get a ghastly incorrect...

Hello all! I'm hoping you will be able to direct me to sources of raw income1 / employment data. Hopefully this thread can be a help to others who have similar needs in the future, as well. (I did a quick search for a similar thread and didn't find anything - please correct me if I'm wrong.)...

Homework Statement I have to prove that ## \int e^{\frac{x^2}{-2}}dx ## from +∞ to -∞ = ##\sqrt{2\pi} ## Homework Equations N/A The Attempt at a Solution My GSI went from 1) ## \int e^{\frac{x^2}{-2}}dx ## from +∞ to -∞ = ##\sqrt{2\pi} ## to 2) ## (\int e^{\frac{x^2}{-2}}dx)(\int...

Homework Statement In a study to estimate the proportion of residents in a city that support the construction of a new bypass road in the vicinity, a random sample of 2025 residents were polled. Let X denote the number in the sample who supported the proposal. To estimate the true proportion in...

Homework Statement The wait time (after a scheduled arrival time) in minutes for a train to arrive is Uniformly distributed over the interval [0,12]. You observe the wait time for the next 95 trains to arrive. Assume wait times are independent. Part a) What is the approximate probability (to 2...

Hello! Dr. David Tong, in his statistical physics notes, derives the Boltzmann distribution in the following manner. He considers a system (say A) in contact with a heat reservoir (say R) that is at a temperature T. He then writes that the number of microstates of the combined system (A and R)...

Homework Statement Suppose that X has normal distribution. Find the distribution of n(Sample Mean - μ)2/σ2. The Attempt at a Solution I honestly have no idea where to begin with this problem. Any ideas?

A negative charge cloud distribute as a ellipsoid and a positive point charge situated at the centre of the ellipsoid.What should be the dipole moment of charge distribution.I mean, if the negative charge distribution is spherical and positive point charge at the centre then surely dipole moment...

Homework Statement The life times, Y in years of a certain brand of low-grade lightbulbs follow an exponential distribution with a mean of 0.6 years. A tester makes random observations of the life times of this particular brand of lightbulbs and records them one by one as either a success if...

Homework Statement A cylindrical distribution of charge ρ = α/sqrt(r) where α = 2 µC/m^(5/2) extends from 0 cm to 9.3 cm (has radius 9.3 cm). Concentric with this is a dielectric shell with k = 5.44 of inner radius 16.6 cm and outer radius 24.9 cm. What is the electric field at 3.53 cm, 12.6...

Hi all Maybe a quick question! After the big bang and inflation, a little while later there is the mass annihilation event where 10 billion matter particles and 10 billion anti matter particles annihilate, sending out energetic photons. For each 10 billion annihilation events there is one...

Homework Statement In thermal equilibrium, the particle in a gas are distributed in velocity space according to the Maxwell distribution f(v) = A*exp(-mv^2/(2KT)) What is the average velocity ? What is the most probable velocity ? Homework Equations <v> = ∫∫∫vf(v)d3v = (0 to infinty)...

I have one dimensional binned data that has a peak to which I need to fit a distribution, such as Gaussian or Lorentzian, that is described with four parameters, height, width, centroid position and the background. The problem is that the counts per bin are low and the peak is only 5-6 bins wide...