Uniform Definition and 1000 Threads

Let x(1),...,x(N) all be independent uniformally distributed variables defined on (0,1), i.e. (x(1),...,x(N)) - U(0,1). Define the random variable y(i) = x(i)/(x(1)+...+x(N)) for all i=1,...,N. I’m looking for the pdf of the random variables y(1),…,y(N). Has anyone come across such random...

I understand that the magnetic field at points inside the solenoid is the vector sum of the B field due to each ring. How can the field inside be uniform then since if you consider just one loop in the solenoid the value of the B field is different at different points in that circle or loop.

Problem (a) Derive and expression (using cylindrical coordinates) for the drift velocity of a particle of mass m and charge q in a uniform vertical magnetic field B\hat{z} when the particle is located at a perpindicular distance p from a long, straight vertical wire carrying a line charge...

This is something that when I see the work done it makes sense, but I find it difficult to do myself. I'm also aware there is an explicit formula for doing this but that involves Jacobians and a well-defined inverse, so I think it's more intuitive to do it step-by-step. Problem: Suppose $X...

Homework Statement I will honestly be so grateful if someone can explain this to me. I am studying the Reynolds transport theorem, particularly mass conservation. I have read over my notes and I really do not understand how to calculate the mass flow rate through the control surface if it...

Three people are balanced on a uniform seesaw -- Torque Homework Statement Three people are balanced on a uniform seesaw which has a weight of 150 N as shown in the figure. Find the mass of person B and the normal force acting on the fulcrum. Homework Equations Tcw=Tccw The...

Homework Statement We had to prove that an integral didn't exist by computing upper and lower sums. It was for f(x)=x for rational 0 for irrational Homework Equations The Attempt at a Solution Lower was easy, it's just 0 (inf of any interval is 0). But the upper...

Homework Statement A uniform steel bar swings from a pivot at one end with a period of 1.3 sec. Solve for Length of bar Homework Equations T=2pi*sqrt(L/g)The Attempt at a Solution since the period is 1.3 seconds, I just plug in 1.3 for T and 9.8m/s^2 for g and solve for L i get L= .42m, which...

Hi, I'm trying to find a probability distribution (D) with the following property: Given two independent stochastic variables X1 and X2 from the distribution D, I want the difference Y=X1-X2 to have a uniform distribution (one the interval [0,1], say). I don't seem to be able to solve it...

Homework Statement A uniform rectangular block of length 37.0 cm is placed so that its centre of mass is a distance of 1.50 cm away from the edge of the table. Since its centre of mass is still over the table (i.e. not sticking out past the edge), the block is stable. An identical block is...

Homework Statement . Suppose you are pushing a 60 N uniform crate at rest with a horizontal force of 40 N exerted at the top as shown. The crate is a cube with length of L. If the coefficient of static friction between the crate and floor is 0.75, which statement below is correct? (Hint...

Homework Statement Charge of uniform density 4.50nC/m is distributed along the circle of radius R. What is the electrical potential (relative to zero at infinity) at the centre of the circle? Answer: 254V Homework Equations electric potential: V=kQ/r The Attempt at a Solution Because the...

Homework Statement A uniform thin rod with mass 4.59 kilograms pivots about an axis through its center and perpendicular to its length. Two small bodies with a mass of 0.543 kilograms, are attached to the ends of the rod. What is the length of the rod such that the moment of inertia of the...

Homework Statement A ferris wheel with a radius of 14.0 m rotates at a constant rate, completing three revolutions in 50.0 s. What is the apparent weight of a 60.0 kg passenger when she is at the top of the wheel? Given choices: 532 N, 452 N, 562 N, 625 N, 469 N Homework Equations...

hello (pardon me if this is a lame question, but i got to still ask) If a function is uniformly continuous (on a given interval) then is it required for the derivative of the function to be continuous? I was thinking as per the definition of Uniform continuity, f(x) should be as close to...

Homework Statement Imagine two clocks that both perform uniform circular motion of radius a in the x-y plane, but in opposite directions: xμ(u) ={t, a cos(ωt),±a sin(ωt), 0}. Suppose these clocks are synchronized to agree when they are coincident at x = a at t = 0. How much time elapses until...

Homework Statement Typical semiconductor fabrication technologies employ copper (ρ ~ 15.7nΩm; μr ~1) as the interconnect material. A process is designed for a clock frequency of 1GHz, has interconnect cross sections ranging between 35nm x 70nm and 0.18um and 90nm. Quantitatively determine...

The sun is far, far away. The Earth is far, far away. No stars. Nothing but unbounded spacetime. And three rockets. Rocket #1: Velocity (according to its odometer): 700 mph Towards Earth (constant speed) Rocket #2: Accelerating (according to its odometer) to 800mph towards some galaxy far away...

Homework Statement http://gyazo.com/55eaace8994d246974ef750ebeb36069 Homework Equations Theorem III : http://gyazo.com/af2dfeb33d3382430d39f275268c15b1 The Attempt at a Solution At first this question had me jumping to a wrong conclusion. Upon closer inspection I see the...

It seems like there is no such thing as uniform motion. Example: I just took my pup to the beach. She crashed into many waves. We're back and she's asleep (at rest). However, her position in spacetime is changing because she's attached to the earth, which is moving, and the Earth is...

If all motion is relative, then why is the general theory of relativity so much more dense with mathematics? I'm not asking you to explain the math--there is no way I would ever grasp that. What I'm confused on is why non-uniform motion (accelerated or decelerated motion) is so different from...

f(x)=1, θ-1/2 ≤ x ≤ θ+1/2 Given that Z=(b-a)(x-θ)+(1/2)(a+b) how would you show that Z has a continuous uniform distribution over the interval (a,b)? Any help would be much appreciated.

Homework Statement Suppose that ##s_n(x)## converges uniformly to ##s(x)## on ##[b, ∞)##. If ##lim_{x→∞} s_n(x) = a_n## for each n and ##lim_{n→∞} a_n = a## prove that : ##lim_{x→∞} s(x) = a## Homework Equations ##\space ε/N## The Attempt at a Solution I see a quick way to do this one...

Homework Statement At t1 = 3.00 s, the acceleration of a particle moving at constant speed in counterclockwise circular motion is a1=(6m/s2)i+(5m/s2)j At t2 = 4.00 s (less than one period later), the acceleration is a2=(5m/s2)i-(6m/s2)j The period is more than 1.00 s. What is the radius of...

Could any here smart people help me with the Lab question: 3. Why do we measure the period by timing 25 revolutions? Why not one revolution or 100 revolutions? This is from http://www2.sunysuffolk.edu/denicog/labs/lab11_132.pdf Lab from Uniform Circular motion. Thank you so much!

Homework Statement Prove that if f is uniformly continuous on a bounded set S, then f is a bounded function on S.Homework Equations Uniform continuity: For all e>0, there exist d>0 s.t for all x,y in S |x-y| implies |f(x)-f(y)| The Attempt at a Solution Every time my book has covered a...

Which wood cross sectioπ caπ carry hïghest uπiform load Homework Statement Homework Equations Moment of inertia for rectangle I=(1/12)bh3 τ=(VQ)/(I*b) σ=(MV)/I The Attempt at a Solution I started by finding reactions at B and C Then drew the sheer and moment diagrams (to save...

Hello. So I was wondering that when you shoot an electron through an uniform magnetic field, obviously Lorenz force starts to skew the path to that corkscrew shape that we all know. But then there is an acceleration towards the center of the circle, and if the the velocity of the electron...

Homework Statement I would like to use the Weierstrass M-test to show that this family of functions/kernels is uniformly convergent for a seminar I must give tomorrow. H_{t} (x) = \sum ^{-\infty}_{\infty} e^{-4 \pi ^{2} n^{2} t} e^{2 \pi i n x} . Homework Equations The Attempt at a...

Homework Statement The proportion of time x that an industrial robot is in operation during a 40 hour work week is a random variable wth probability density function f(x)= 2x 0≤x≤1 I already found my E(x) to be 2/3 " Mean" and V(x) to be 1/18 " variance" Here is where things get...

Homework Statement A uniform circular disc has mass M and diameter AB of length 4a. The disc rotates in a vertical plane about a fixed smooth axis perpendicular to the disc through the point D of AB where AD=a. The disc is released from rest with AB horizontal. (See attached diagram) (a)...

Homework Statement An insulating rod having linear charge density l 5 40.0 mC/m and linear mass density m 5 0.100 kg/m is released from rest in a uniform electric field E 5 100 V/m directed perpendicular to the rod (Fig. P25.9). (a) Determine the speed of the rod after it has traveled...

A uniform spring whose unstretched length... A uniform spring whose unstretched length is L has a spring constant k. the spring is cut into two pieces of unstretched lengths L1 and L2, with L1 = nL2. What are the corresponding spring constants k1 and k2 in terms of n and k? The answer is k1...

The field makes an angle θ with side 1 and the area of each face is A. In symbolic form, find the electric flux through (a) face 1, (b) face 2, (c) face 3, (d) face 4 and (e) top and bottom. My professor got: a=EAcosθ b=-EAsinθ c=-EAcosθ d=EAsinθ e= 0 I understant why e=0 but for the...

I am in need for some help for a lab report. The issue has happened because there is a lab of 20 students that is being led by a recently retired NASA physicist trying to lead a team of graduate student (or camel jockeys as he puts it) and the lab instructions are being botched horribly...

A subway trains starts from station A with a uniform acceleration of .5m/s and attains full speed after 50 seconds. It travels at full speed for 120 seconds then is brought to rest at station by by the application of brakes which provides a acceleration of -2.50. Find the distance between A...

Homework Statement Two concentric spherical shells carrying uniformly distributed charges +Q and -Q at radii a and b, respectively (b>a). Now, they are immersed in a uniform magnetic field pointing along the z-axis. Find the angular momentum of the fields.Homework Equations No need. (I know...

Hi! The velocity field as a function of poisition of an incompressible fluid in a uniform acceleration field, such as a waterfall accelerated by gravity can be found as follows: The position is \vec{x}. The velocity field is \vec{v} = \frac{d\vec{x}}{dt}. The constant acceleration field...

Homework Statement A point charge q, moving with uniform velocity \vec{v} = v \hat{z}, in the laboratory frame called \cal{K}. The charge is in the origin of the system at time t=0. Homework Equations Find scalar potential \Phi and vector potential \vec{A} both in the frame in which the...

Homework Statement It is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral motion as uniform circular motion combined with a constant upward velocity. Assume a bird completes a circle of radius 6.00m every 5.00s and rises...

Homework Statement A parallel-plate uniform electric field with a strength of 325 N/C is oriented as shown below. An electron (q = 1.6 × 10-19 C, m = 9.11 × 10-31 kg) is released (from rest) inside the field and moves 3.2 cm to the left. What is the final speed of the electron at the end of...

How is uniform electric field produced? Consider two parallel plates with one +ve and the other -ve. The field depends on the charge producing the field and the distance to a point in between the place. However, in this case, the distance decreases and hence the field decreases and is not...

Homework Statement An electron is projected with an initial speed v_0 = 1.60 * 10^6 m/s into a uniform field between two parallel plates, separated by a distance of 1cm, and each plate is 2cm across. Assume the field outside the plates is zero. The electron enters the field at a point midway...

How exactly does radius affect centripetal acceleration? In one formula we have (a=v^2/r) which implies inversely proportional, while in the other we have (a=(w^2)*r) which implies directly proportional. I understand that increasing r increases velocity (v=w*r) which means the right answer is...

Hi, I don't know what I'm doing wrong but these significant figures seem to be screwing me up. Problem: A bike rider accelerates constantly to a velocity of 7.5 m/s during 4.5 s. The bike's displacement is +19 m. What was the initial velocity of the bike? The textbook says the answer is 0.94...

Homework Statement A very small sphere with positive charge 6.00uC is released from rest at a point 1.20cm from a very long line of uniform linear charge density 4.00uC/m.What is the kinetic energy of the sphere when it is 4.80cm from the line of charge if the only force on it is the force...

Homework Statement A car decelerates uniformly and comes to a stop after 10 s. The car's average velocity during deceleration was 50 km/h. What was the car's acceleration while slowing to a stop? {Since the acceleration is UNIFORM (constant), use vavg = (v0 + v)/2... } Homework Equations The...

Homework Statement A rod 16.0 cm long is uniformly charged and has a total charge of -21.0 µC. Determine the magnitude and direction of the electric field along the axis of the rod at a point 42.0 cm from its center.Homework Equations The Attempt at a Solution The equation I am advised to use...

Homework Statement A boy ties a rock to a 0.95 m string and swings it in a horizontal circle directly over his head so that it completes one revolution every 0.75 s. What is the tension in the string? So we know r and we can calculate V, but that's all I can deduce Homework Equations...

Homework Statement Let Yn be uniform on {1, 2, . . . , n} (i.e. taking each value with probability 1/n). Draw the distribution function of Yn/n. Show that the sequence Yn/n converges in distribution as n → ∞. What is the limit? Homework Equations So Yn has c.d.f Yn(x) = |x|/n where |x| is...