Distribution Definition and 1000 Threads

Assume the jet is straight but the radius of the jet varies over it's length (like a jet of water falling which narrows due to gravitational acceleration). Also ignore viscosity. A pressure gradient would be required to accelerate the fluid radially. Because during an expansion transformation...

Hi, I was just thinking about different ways to use the Fourier transform in other areas of mathematics. I am not sure whether this is the correct forum, but it is related to probability so I thought I ought to put it here. Question: Is the following method an appropriate way to calculate the...

1) Since I want at least ##6## flights to come within ##2## hours, then the time interval between each should be, at worse, ##2/6=1/3## hours, and the probability is ##P(X\leq1/3)=1-e^{-1/3}##. 2) The probability that at best 5 airplanes arrive at the airport is...

Can someone help me on this question? I'm finding a very strange probability distribution. Question: Suppose that x_1 and x_2 are independent with x_1 ~ geometric(p) and x_2 ~ geometric (1-p). That's x_1 has geometric distribution with parameter p and x_2 has geometric distribution with...

Let ##X_1 X_2 X_3 ## be three independent random variables having Normal(Gaussian ) distribution, all with mean ##\mu##=20 and variance ##\sigma^2##=9. Also let ##S=X_1+ X_2 +X_3## and let ##N## be the number of the ##X_i## assuming values greater than 25. ##E\left[N\right]##=? I did not...

In the Aschcroft & Mermin solid state book there is a curve to compare F.D and M.B distribution. I can't understand the concept of M.B curve; what does mean exactlly when x =0? It means the probability of zero energy for particles is most or ...?

Need some help on how to solve the integration formula for Maxwell speed distribution, here is the procedure on how to solve for the kinetic energy: Not familiar with the error function yet, but the result for the kinetic energy integration is...

Just wondered if the power of mags. is decreased, or they are more separated, don't you get a normal distribution ? (I'm in biology) - would you also not have predicted that w. reasonably strong magnets, they will either end one one side or the other ? Thx a lot!

Say I make it so that the 2 coin flips count as a single number 1,2,3,4 representing head-head, head-tails, tails-head, tails-tails. Then what do I do? I'm just lost as to how I would even approach this problem.

I sort of understand the meaning of this integral, but I don't know how to evaluate it. I have never evaluated a volume integral. It would be very helpful if someone could explain in other words what this integral means and give an example evaluating it. This is from Purcell's Electricity and...

Confused and not sure if it is correct, but please do correct my steps. We let event B be that there are at least 3 customers entering in 5 minutes. Hence P(B) = 1- P(X=0)- P(X=1) - P(X=2) = ##1- \dfrac{e^{-5}5^{0}}{0!}-\dfrac{e^{-5}5^{1}}{1!}-\dfrac{e^{-5}5^{2}}{2!} ## = 0.8753... Now we let...

How can I prove the Cauchy distribution has no moments? ##E(X^n)=\int_{-\infty}^\infty\frac{x^n}{\pi(1+x^2)}\ dx.## I can prove myself, letting ##n=1## or ##n=2## that it does not have any moment. However, how would I prove for ALL ##n##, that the Cauchy distribution has no moments?

Hi, I want to know how the highlighted steps are arrived at in the first page. What are \(R_X (y), R'_X (y),F'_X (0) ? \)How \(R_X (0) = 1 ?\) Solution to differential equation should be \(R_X (y)=K*e^{\int{R'_X (0) dx}}\) But it is different. How is that? What is $-R'_X...

The charges are q1,q2 & q. P,Q,O1,O2 refer to positions only. This is a conducting sphere with cavities containing charges. I'm interested in knowing how the charge should be distributed in the sphere. I know the charges induced on the charges of the sphere should be equal and opposite to the...

Could you help me about the derivation of inverse gaussian distribution? During my search I encountered that it was derived by schrödinger as a result of differential equation solution but I can not find his derivation on internet...

I have the following integral (in Maple notation): Int(exp(c[0]*ln(y)/a[0]+c[1]*M*ln(M-y)/a[1]), y = 0 .. M); with (in Maple notation): 0<a[0], 0<a[1], 0<c[0], 0<c[1], 0<y, y<M, 0<M. What is the solution of this integral? I suspect that the solution has something to do with a beta distribution.

How to visualize charge distributions in COMSOL, like showing + or - charges on a surface or a bulk in postprocessing?

I quite understand the fact the EPE (Electrical Potential Energy) of a system of two charges are U = k*qQ/r, Q is fix. however when it comes to three charges i get lost. because my reasoning is : if q1 is fix then the EPE of the system when q2 is brought is U2 = k*q1*q2/r12, when q3 is brought...

What percentage of the universe’s A) total mass —including dark matter— and B) radiation energy is estimated to reside in: Inter-galactic space covering i) inter-galactic medium and ii) distinct inter-galactic astronomical objects; and Galaxies covering iii) inter-stellar gas clouds, iv) stars...

Let’s say we have a unit volume of some fluid in a column on the Earth surface. Let ##\mathbf F## be the gravitational force that acts on the unit volume of the fluid. Consider a small volume element ##\Delta \tau## in the fluid and let’s assume it to be a cuboid with dimensions ##\Delta x##...

Why it's not a practice to use such busbar spacing insulator arrangement as it's showed in the picture from attachment (one busbar above other)?

i did not get how the professor came to such result. In particular: in order to evaluate P[x+y<=z] solved a double integral of the joint density. What i am not getting is did i choose the extreme of integration in order to get as result ##\frac {z^2} {2}##

I am not sure about finding the limit of the integral when it comes to finding the CDF using the distribution function technique. I know that support of y is 0 ≤y<4, and it is not a one-to-one transformation. Now, I am confused with part b), finding the limits when calculating the cdf of Y...

In a park , 200 foxes are tagged. In 100 sighting, 14 were tagged. Estimate the size of the fox population ? This is how approached . 200 tagged : Population 14 tagged : 100 (200x100/14)= Estimated Population = 1,429 I wonder if this is right !

First of all, I didn't know whether to pick this subforum or the engineering/compsci one, I understand this might need to be moved to a more appropriate subforum. The general approach is fairly obvious, use implicit method to construct the tridiagonal matrix for Thomas method and solve. However...

When two BHs collide the resulting single BH bulges and contorts until it settles down to a stable state. 1) Does this mean that during this 'settling' period the mass internal to the merged BH is not (yet) a singularity, but instead two 'singularities' spinning down around each other in...

I need guidance on part c, finding the cdf/pdf of Y. I understand that for X>3, Y=6-X and for X<3, Y=X. For X = 3, Y=3 For part b, I got P(Y>y)= (3-y)/3, for 0≤y<3 Now for part c, I know P(Y>y) relates to the cdf. But the definition of cdf relates to P(Y<y), so I'm guessing I have to do...

I'm currently programming lots of physics simulators in DHTML, and my next step would be simulating a perfect gas behavior at a molecular point of view, bouncing inside of an HTML canvas. For this reason, I came across "Maxwell-Boltzmann's law of distribution"(for speed, which I only studied...

To begin with, I can first let ##T(x,y) = X(x) Y(y)## to be the given solution. With this, I can then continue by writing: $$Y \frac{\partial^2 X}{\partial x^2} + X \frac{\partial^2 Y}{\partial y^2} = 0$$ $$\Longrightarrow \frac{1}{X} \frac{\partial ^2 X}{\partial x^2} + \frac{1}{Y}...

I have written the following source code: using System; public class CommonDistributions { public static double Uniform(Random random) { return random.NextDouble(); } static double Gaussian(Random random) { return Math.Sqrt(-2 * Math.Log(Uniform(random))) *...

The attached image shows the text I am following. I get that the 3-D pdf F can only depend on the speed v. I also understand that if f_x , f_y, f_z are the pdfs of the individual components of velocity, then rotational invariance requires them to all be the same function f_x = f_y = f_z = ϕ...

I'm just going to skip some of the step since I only need help with understanding the last part. After rearranging the equation stated at "Relevant equation" (and skipping some steps) we will get: E * 4*pi*e0*R^2 = integral pv * 4*pi*R^2 dR E = 1/(4*pi*e0*R^2) * 4*pi * integral pv*R^2 dR E =...

Here's the problem: A chef made 500 cookies randomly mixed with 1000 nuts including 600 almonds and 400 hazelnuts in which each nut is the same size. Suppose the number of pieces of nuts in a piece of cookie follows a Poisson distribution. (a) Suppose cookies are randomly selected one-by-one...

I was reading about the Debye-Huckle theory for electrolytes solutions (https://en.wikipedia.org/wiki/Debye–Hückel_theory). In all the books, notes, and in the wikipedia age too, there is this statement that troubles me: Shouldn't I have the "normalization factor" (i.e ##1/Z##) in the above...

Hey there, the task I'm working on is written below. Find the quadrature distribution ρ(q), for an optical mode being in the coherent state |α>. Hint: use ∑Hn(x)*(t^n)/(n!) I really am struggling with this type of tasks :D I tried to follow a solved example that I found in my workbook, but...

Hello. I need some guidance on how to find the fraction of molecules with KE between K1 and K2 from the Maxwell kinetic energy distribution function. Here's an link to an earlier post where the speed distribution was integrated, how will I proceed with the kinetic energy distribution...

I want to calculate the kinetic energy distribution amongst let's say nitrogen molecules by using M.K.E.D, but not sure where to start. I posted a picturefrom my physics book where the formula is shown, there was no example in the book. As for g(K), is K the same as the kinetic energy formula...

If we assume the energy of particles in an ideal gas follows a Boltzmann distribution, then the energy distribution function can be defined as below: , where k_B is the Boltzmann constant Since the energy of particles in an ideal gas are assumed to only consist of translational kinetic energy...

My answer was +Q/3. I was assuming that the charges would distributed themselves completely. But, apparently, I'm wrong? For example, if there were 12##e^-##s on Sphere C, then, in the first step in the system: the ##e^-##s would balance out until each sphere has 4 ##e^-##s each? What am I...

John has baked 31 cupcakes for 5 different students. He wants to give them all to his students but he wants to give an odd number of cupcakes to each one. How many ways can he do this? Brute-forcing will take about a whole day, I think. If 4 students receive 1 cupcake and the other one receive...

Suppose I have an exact microscopic distribution function in phase-space defined as a sum of delta-functions, i.e $$F( \mathbf x, \mathbf v, t) = \sum_{i} \delta( \mathbf x - \mathbf x_i ) \delta (\mathbf v - \mathbf v_i )$$ Can I conclude that, in absence of creation/destruction of particles...

This is the problem, first time i am attempting the Ampere's law problem From the above question this is my attempt, the picture is ∫B.ds = μ*Ienc; ----> Ampere law , where Ienc is the current enclosed in the amperian loop. I assume the circle as the amperian loop, is it correct? Can i...

a. P(X = 3) = (4/6) x (4/6) x (4/6) x (2/6) = 8/81 b. X ~ Geo (2/3) Is this correct? Thanks

In these lecture notes about statistical mechanics, page ##10##, we can see the graph below. It represents the distribution (probability density function) of the kinetic energy ##E## (a random variable) of all the gas particles (i.e., ##E=\sum_{i}^{N} E_{i}##, where ##E_{i}## (also a random...

Hey! :o We are given a list of $300$ data which are the square meters of houses. I have calculated the mean value and the median. After that we have to say something about the symmetry of the distribution. For that do we have to make a diagram from the given data? Is there a program to do that...

This is not really homework, but I'm having trouble understanding it intuitively. I came across this when learning about the space charge layer of a diode. The solution I know simply uses the 1D form of Gauss's law: ##\vec{\nabla} \cdot \vec{E}## = ##\dfrac{\rho}{\epsilon_0}## becomes...

Why tossing a coin three times is said to have binomial distribution? I'm little bit confused.

Problem: Let $X_n$ be independent random variables such that $X_1 = 1$, and for $n \geq 2$, $P(X_n=n)=n^{-2}$ and $P(X_n=1)=P(X_n=0)=\frac{1}{2}(1-n^{-2})$. Show $(1/\sqrt{n})(\sum_{m=1}^{n}X_n-n/2)$ converges weakly to a normal distribution as $n \rightarrow \infty$.Thoughts: My professor...

I know that I'm supposed to use Weibull, but why does my teacher take the middle value, 5 m/s? Should one not integrate the formula and the use 4,5 and 5,5 as limits? This is what he has done: He then writes: makes a guess of an interval of 1 m/s and get: To be honest, I really don't...