Distribution Definition and 1000 Threads

Homework Statement Evaluate \int_C \vec{F} \cdot d\vec{r} Where \vec{F} is the field generated from a circular thread of radius b in the xy plane, with magnitude j in the direction \hat{\varphi} (i.e. not along the curve, I take it) C: (x,y,z) = b(1+ \cos{\alpha}, 0, \sin{\alpha}) 3. The...

Hey all, I've had this point of confusion for a bit and I have thought that with time I may be able to clear it out myself. Nope, hasn't happened. I think I need help. Let us say we have the following \phi_{k+1}=\phi_{k}+v_k where, v_k\overset{iid}{\sim}\mathcal{N}(0,\sigma^2) and...

Homework Statement The relationship between the expected value and the variance for a particular normal CDF is known to follow the rule ##E(X)=arcsin(ln(Var(X)))##. Given that ##Pr(0.32<Z<2.32)=Pr(12.9<X<74.275)##, determine the possible values of the mean and the standard deviation correct to...

speed? This question emerged in my mind while studying a discrete and continuous mathematical model of a falling slinky. In the discrete model, we suppose an instantaneous interaction between mass points at a distance, so the action propagates through the chain of mass points with infinite...

it's stated that general theory of relativity describes gravity a consequence of the curvature of spacetime caused by the uneven distribution of mass/energy...what caused the uneven distribution of mass/energy? And if the universe is said to be expanding what is the universe expanding to, and...

I have a set of data which are probably convolutions of a Cauchy distribution with some other distribution. I am looking for some model for this other distribution so that a tractable analytic formula results. I know that the convolution Cauchy with Cauchy is again Cauchy, but I want the other...

Homework Statement This is more of a general question, but a simple example would be find the force on a test charge q at the center of a ring of charge with a total charge Q and a charge distribution given as λ(θ) =ksin(θ) where θ is measured clockwise with respect to the positive x-axis. The...

I've searched for a formula of galaxy mass Distribution formula along the radius, often the papers say: ρ∝ex ( ρ is the surface density, x is distance from the Center of the galaxy). is it correct without DM? Or is there any other correct formula?

I'm an A level student currently trying to understand the behaviour and properties of neutrinos, and wanted to check that I've understood the basics of neutrino properties. As neutrinos are half-integer spin particles, can the Fermi-Dirac distribution be used to calculated the probable...

Hi everyone! I have perhaps a basic question, but I can't dealt with it. I have a rectangular sample 50x150mm of let's say wood. The sample is compressed from the top over the width of 4mm. I know the shortening of the sample at 70 mm from the bottom (from experimental testing) and I know the...

Suppose you have a lavatory with 4 cubicles, in a company that has 30 employees using that lavatory. Knowing that on average an employee spends 10 minutes in the cubicle, what is the probability that, at any given time, 0, 1, 2, 3 or 4 cubicles are in use? And what would be the average waiting...

Hello! Let E_1, E_2, \ldots, E_n be n allowed energy levels for a system of electrons. This system can be described by the Fermi-Dirac distribution f(E). Each of those levels can be occupied by two electrons if they have opposite spins. Suppose that E_1, E_2, \ldots, E_n are such that...

Hello! Maybe someone will be able to suggest something about the following quite simple problem: 1D problem on axis "X". Particle moves only along "X" axis and starts its motion from X=0. However, when "X<0" particle disappears. Particle is influenced by some kind of force in such way that we...

I'm not quite sure how to describe this phenomena but in my town we have a large boardwalk structure and it is closed off almost entirely underneath by a sea wall. this leaves slits on top with the boards and slits near the top of the sea wall where a concrete beam will pass through. at certain...

Homework Statement In computing the average kinetic energy of a molecule obeying Maxwellian distribution one use the formula ½mc2 .Calculate the percentage error incurred in the calculation. The Attempt at a Solution Here c is the average velocity of a molecule obeying Maxwellian distribution...

Homework Statement Let ρ(r)= Qr/πR4 be the charge density distribution for a solid sphere of radius R and total charge Q.For a point 'P' inside the sphere at distance r1 from the centre of the sphere, the magnitude of electric field is ? A) 0 B) Q/4πε°(r1)2 C) Q(r1)2/4πε°R4 D)...

Had an argument with a few guys at the gym today. I told them that loading a barbell with 100 on each side instead of 2 45s and a 10 causes more pressure on your spine. This example is in reference to someone performing a low bar squat in which the bar has contact points across the entire back...

On this page: http://galileo.phys.virginia.edu/classes/252/kinetic_theory.html From the text beginning with "Let us now figure out the distribution of particles as a function of speed.", whats the reasoning behind multiplying a radial distribution with a volume? Is it the same thing as...

[MENTOR note] Post moved from General Math forum hence no template. Assume that a random variable follows a normal distribution with a mean of 80 and a standard deviation of 24. What percentage of this distribution is not between 32 and 116? My approach is to calculate the Probability for (mean...

Homework Statement The time Rafa spends on his homework each day is normally distributed with mean 1.9hrs and standard deviation σ. On 80% of these days he spends more than 1.35 hours on his homework. i. find the value of σ ii. find the probability that Rafa spends less than 2 hours on his...

Homework Statement [/B] I have got data x, which is formed like uniform distribution. After using discrete low pass filter I got output data u, which is Gauss distribution. What is explanation, why using that filter, we from uniform distribution can get Gauss distribution? Homework...

Why are so many phenomena well described by the normal distribution? For example: the height of 18 year old males in Sweden, the weight of apples on a particular tree, the volume of coke cans (supposed to be 33 cl), etc. etc. are all well described by the normal distribution. How come? A...

The analysis of the distribution of spins for a paramagnetic solid in a B field shows that the probability of a dipole being aligned/anti-aligned with the B field ##\to 0.5## as ##T \to \infty##. The intuitive justifications that I've read say that this is "expected" as thermal motion tends to...

I don't get this shear force distribution stuff. In my drawing A is sort of a free body diagram. Load W is dead center of a beam, and of course this force is supported at either end by two reaction forces.with a value of W/2. B is a shear force diagram. For points < L/2, shear force is...

Homework Statement Consider a long, cylindrical charge distribution of radius R with uniform charge density ρ. a) Using Gauss’s law, find the electric field at distance r from the axis, where r < R b) Using Gauss’s law, find the electric field at distance r from the axis, where r > R...

Homework Statement Hi, I am working making a soccer game in a game engine and encountered a problem with calculating what velocity a ball has to be kicked into get from A to B. the ball has to be passed (on a flat surface with friction coefficient of 0.35) from point A to point B, but since...

Hi everyone, I am self-studying Electricity and Magnetism. I have a good grasp in Calculus, but still I am confused on how to figure out volumes of arbitrary figures(rest is easy). I know it's a bit silly. I mean how do we know how to choose a figure (like in case of hemisphere, you imagine...

Suppose that a given population is endowed with a pair of characteristics T and K. Let's think of these characteristics as random variables (T,K)∼BiNormal((μT,μS),(σT,σS),ρ) I observe the realisations of T for a sample consisting of those individuals with K<a, where the selection threshold a...

Homework Statement I'm having trouble understanding setting up a frequency distribution. I am confident I am doing it right, but the book I'm using differs when calculating width. The problem gives a bunch of numbers representing the number of counties, divisions, or parishes for each of the...

There is a well-known analysis of the distribution of particles by height in an isothermal atmosphere. It states that the probability of finding a particle at height ##h## is ##p(h) \propto e^{-\beta mgh}##, and then goes on to state that the number of particles at height ##h## is ##n(h) \propto...

Right now I'm having a problem with a statistics problem. More specifically with a binomial distribution problem. The problem says: There is a family composed by 8 children. Calculate the probability that 3 of them are girls As far as I know, binomial distribution formula says...

I'm having trouble understanding the role of the volume of velocity space when deriving the Maxwell-Boltzmann speed distribution. 1. If we wish to compute the speed distribution from the velocity distribution we work with, say, p(v) dv \propto v^2e^{-av^2} dv where the ##v^2 dv## comes from...

Homework Statement A fair coin has a ##1## painted upon one side and a ##2## painted upon the other side. The coin is tossed ##3## times. Write down a sample space for this experiment. Let ##X_1## be the sum of the numbers obtained on the first ##2## tosses and ##X_2## be the sum of the numbers...

Homework Statement The random variable ##(x,y)## has density ##f(x,y) = ce^{-(ax+by)}## for ##0\leq y\leq x\leq 1##, with given constants ##a > 0##, ##b > 0##. 1. Compute the constant ##c##. 2. Find the conditional probability density ##f_y(y|x)##. 3. Compute the regression curve of ##Y## on...

I've calculated the joint distribution, XY_PDF(x,y) of random variables X and Y (both coming from a distribution N(n) = C*e^(-K*n^2)). I use XY_PDF(x,y) to calculate the joint distribution AR_PDF(a,r) of the random variables A (angle) and R (radius), with the PDF method and the Jacobian. Since...

I'm looking to measure the weight of an tennis racket at different lengths. Obviously If I stick it on the scale it will give roughly the sam,e weight no matter if I put the whole racket on, or a third of the racket. Would there be a way I could measure the weight, of say the first third of an...

Okay, my online class has posed another word problem and I cannot seem to understand this week's material or how to formulate a solution. Here it is: Imagine you are in a game show, a money give-away! There are 4 prizes hidden on a game board with 16 spaces. One prize is worth \$4000...

hi, so my lecturer decides to give me manic depression by sending me on a wild goose chase. what is the general form of a plot of Ψ, Ψr2 and r2Ψ versus r for both Ψ2s and Ψ2p orbital... am not even sure i said it right So far I have only gotten the Ψ2r2 versus r

hi, so my lecturer decides to give me manic depression by sending me on a wild goose chase. what is the general form of a plot of Ψ, Ψr2 and r2Ψ versus r for both Ψ2s and Ψ2p orbital... am not even sure i said it right

i have a question, why is the plot of r2(Ψ2p)2 not a good representation of the probability of finding an electron at a distance r from the nucleus in a 2p orbital

Homework Statement A student sits a test and is told that the marks follow a normal distribution with mean 100. The student receives a mark of 124 and is told that he is at the 68th percentile. Calculate the variance of the distribution. Homework Equations...

I modeled a simple cantilever rectangular beam in Patran of (L,W,H = 100, 6, 4) with Hexa8 elements and applied a vertical shear load (upwards) of some magnitude at the free end. Ran in Nastran and plotted the vertical shear stress distribution on a cross-section in middle of length (in order...

Homework Statement Using direct integration, compute the electric field at the point (0,0,Z) of a semi-espherical (z > 0) charge distribution of radius R < Z and density ##\rho=constant## having a spherical hole of radius ##r_h<R## centered at (0,0,##r_h##). Homework Equations Coulomb's law...

I Have a Dumb Question. If Electricity Supplied from Substation to Feeder to Transformer and Under Transformer If There Are Many Consumers. Assuming That many Consumers Went on for a Holiday, Does Utility Still Pay for the Electricity to the Generation company for the Electricity they Supplied...

Homework Statement The Weibull distribution is used frequently as a lifetime distribution and is so is used a lot in survival analysis. It can be parameterised as:##f(x;\lambda,k) = \frac{k}{\lambda}\left(\frac{x}{\lambda}\right)^{k-1}e^{-\left(\frac{x}{\lambda}\right)^k}## for ##x\geq 0## &...

Hi all, I am analysing the flow of water in a subsea pipe, and have been getting stuck in trying to solve the energy equation to plot a temperature distribution across the pipe diameter I have derived the equation as such seen in my attachement. But my main question is how should/would I...

Homework Statement Show the steps needed to obtain the equation for average molecular speed, cavg=√8RT/πM from the integral (from negative infinity to infinity) ∫v*f(v)dv where f(v) is the Maxwell distribution of speeds function f(v)=4π*(M/2πRT)1.5v2e-Mv2/2RT M is the molar mass of the...

This is a question about transforming a probability distribution, using the blackbody spectrum as an example. Homework Statement An opaque, non-reflective body in thermal equilibrium emits blackbody radiation. The spectrum of this radiation is governed by B(f) = af3 / (ebf−1) , where a and b...

What is electric field distribution around two conductor cable connected to DC power supply? Assume power supply is isolated and not grounded. Assume cable is straight. Case 1: no current runs through the cable. One wire is positive, another – negative. Negative or zero? If we think in terms of...

I'm battled by my thought of interception. The entangled photon between Alice and Bob, suppose the one at Alice's side is already measured to be 1, so the second is heading over to Bob to be 0. Eve gets to it first and measures it to be 0. Knowing its 0, eve prepares a photon of state 0 and...