Normal Definition and 1000 Threads

I am trying to calculate the following sum: vt\Phi(a)+\frac{(vt)^2}{2!}\Phi(\sqrt{2}a)+\frac{(vt)^3}{3!}\Phi(\sqrt{3}a)+\frac{(vt)^4}{4!}\Phi ( \sqrt{4}a)+\ldots where \Phi is the standard normal CDF. v,t,a are constants. A relevant formula is...

Homework Statement Let F be the set of all analytic functions f that map the open unit disc D(0,1) into the set U = \left\{w=u+iv : -2 < u < 2 \right\} such that f(0)=0. Determine whether or not F is a normal family. Homework Equations DEF'N: A normal family on a domain (i.e. open and...

I've been having some trouble with conceptually understanding the idea of a generalized eigenvector. If we have a linear operator A and want to diagonalize we get it's eigenvalues and eigenvectors but if the algebraic multiplicity of one of the eigenvalues is greater than the geometric...

Homework Statement Let G be and group and let N and H be normal subgroups of G with $N \subset H \subset G. Prove that H/N is a subgroup of G/N, and that it is a normal subgroup. Note that aKa^{-1} = {aKa^{-1} | k in K}.Homework Equations The Attempt at a Solution I understand that since H is...

Sorry because I have asked this other times but still not getting a reasonable answer: For bus headway times why in several articles they make assumption of normal distribution?? Generally inter-arrival times are modeled using exponential distribution but in some papers...

Homework Statement I've attached the questionHomework Equations Pr(X<=x)= (x + 0.5 - n*p) / sqrt(n*p*(1-p))The Attempt at a Solution okay so n=1150, p=0.02 , Pr(X<23) =23 + 0.5 - 1150(0.02) / sqrt(1150*0.02*0.98) =0.105316 is that bit right so far. Because it is less than i thought x...

Homework Statement In math 334 one semester, the average student made 1200 computations per month with a standard deviation of 150 computations. Assume that the number of computations is approximated by a normal curve. Find the percent of students making between 1200 and 1600 computations a...

Homework Statement A company pays its employees an average wage of $3.25 an hour with a standard deviation of sixty cents. If the wages are approximately normally distributed, determine the minimum wage of the employees who are paid the highest 5%. Homework Equations z=(x-μ)/σ The Attempt...

Homework Statement An experiment was conducted where a slider with different mass combination is placed on a board. A Newton spring scale is attached to the slider and is pulled horizontally and parallel to the board such that the slider moves at a constant velocity. The applied force...

Hi everybody. For sake of work I have to make an assumption that service time for patients is normally distributed. Normally the doctor has to wait one patient every half hour but anyway this time can vary being less or more. My teacher wants some theory arguments (normal distribution...

Homework Statement If \phi(x,y,z) = x3 + 2xy +yz3 find \nabla\phi at the point P=(1,1,2) and direction of the unit normal to the surface \phi(x,y,z) = 11 at P. Homework Equations The Attempt at a Solution Worked out \nabla\phi to be 5i + 10j + 12k Got |\nabla\phi|= √256 so the...

Hi group, In order to understand the methods of characteristics, I've been reading its wiki entry plus other sources. However, one of the first step of finding the normal surface vector given the PDE remains baffling to me in terms of how it's derived. In short, when provided with a(x...

A woollen mill produces scarves. The mill has several machines each operated by a different person. Jane has recently started working at the mill and the supervisor wishes to check the lengths of the scarves Jane is producing. A random sample of 20 scarves is taken and the length, x cm, of each...

Homework Statement Im trying to construct a function in MATLAB that models linear least squares model fitting through the use of normal equations. Homework Equations Normal equation (A'*A*c)=(A'*y) A= [column vector of all x ; column vector of all 1] y= [column vector of all y] c = [b;a]...

Hi, In Birrel and Davies ch4 they write: \langle \psi|:T_{ab}:|\psi \rangle =\langle \psi|T_{ab}|\psi \rangle -\langle 0|T_{ab}|0 \rangle this is for the usual Mink field modes and vac state. Why does normal ordering reduce to this expression, could anybody point me the way to...

Hello, So I'm in my last semester at my local community college and I'm taking Modern Physics. The class is cool and all, but the material is very hard to grasp. Furthermore the homework questions, (to me), are nearly impossible to complete. It takes me close to thirty minutes just to...

Homework Statement A particle with mass m is trapped inside the infinite potential well: 0<x<L : U(x) = 0 otherwise: U(x) = ∞ ψ(x,t=0) = Ksin(3∏x/L)cos(∏x/L) What energies can be measured from this system, what are the probabilities for these energies ? Homework Equations Schrödinger...

Homework Statement Calculate the frictional force, normal force and coefficient of friction for an 0.2kg object that is lying on a 35 degree incline. Homework Equations Ff= u x Fn F= m x a The Attempt at a Solution I managed to get FN= m x a x cos# = -9.81 x 0.2 x cos35 = 1.61...

A formula for finding the normal vector for curvature is: N=(dT/ds)/(||dT/ds||) Where dT=change in tangent vector ds=change in distance travelled Another fromula was: N=(dT/dt)/(||dT/dt||) What's dt ? Is it the same as ds? I don't think so cause the course notes said that...

Dear Users, For normally distributed random variables x and y's p.d.f.: \frac{1} {\sqrt{2\pi \sigma_x^2}}\exp\left\{- \frac{(x - \mu_x)^2}{2 \sigma_x^2}\right\} and \frac{1} {\sqrt{2\pi \sigma_y^2}}\exp\left\{- \frac{(y - \mu_y)^2}{2 \sigma_y^2}\right\} What will be the p.d.f. of...

Homework Statement http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_s05_qp_6.pdf question no. 6 part ii (Safety regulations state that the pressures must be between 1.9 − b bars and 1.9 + b bars. It is known that 80% of tyres are within...

D is a set of all points (x,y) in R2 distinct from (0,0). I have the funtion f: D --> R which is defined by: f(x,y) = (2xy)/(x2+y2 Im asked to find the equations (in plural) of the tangelnt plane and the normal line to the graph of the function at (1,2) My attempt: I use the tangent plane...

I'm trying to derive an expression for the normal forces on a cars tyres traveling around a circular banked track. Initially I was going to assume the centre of gravity was located longitudinally and laterally centre between all four tyres (so front and rear had the same forces on them). Also...

Let $H\leq G$, where $G$ is some infinite group, and there exists some $g\in G$ such that the set $\{g^n: n\in\mathbb{Z}\}$ is a transversal for $G/H$. Then is $H$ normal in $G$? I suspect not. However, I cannot seem to find a counter-example. (By "a transversal for $G/H$" I mean that 1)...

Homework Statement Homework Equations The Attempt at a Solution

Homework Statement Now, G is a finite group, and P is a Sylow P-Subgroup of G, and H is a subgroup of G with P≤H≤G. So if P is normal in H, and H is normal in G, then P is normal in G. Homework Equations The Attempt at a Solution I know I want to show that gpg^-1 is contained in P...

I am trying to analyse a past series of numbers that flucuates between 107&210 with a normal frequency distribution of mean 162. What is the way to model and project short term future range for trendless but cyclical type of time series?

I have two multivariate normally i.i.d random variables, x and y, that are size n vectors. Let us assume for simplicity that their variances are 1. From these random variables, I form two vectors that contain their means, and denote these mx and my. I know that if mx = my, then W = (mx -...

Homework Statement The small mass m sliding without friction along the looped track shown in the figure is to remain on the track at all times, even at the very top of the loop of radius r. http://session.masteringphysics.com/problemAsset/1057653/6/GIANCOLI.ch08.p090.jpg A)In terms of...

Hey guys. I'm sure some of you are aware of how to analytically integrate e^(-x^2) dx from - infinity to infinity using polar coordinates. I have taken that logic and showed that the integral of the normal distribution( not necessarily standard) integrates to 1 over the entire domain...

Physics lab normal force please help! A 1000-kg car moves at a maximum speed so that it does not skid off the 50-m radius level track. If the coefficient of static friction between the road and wheels is 0.80. What is the maximum speed? Assume that the gravitational constant is 10.0 N/kg =10.0...

Homework Statement Given a parameterized surface: C(u,v) = (3 cos u sin v, 2 sin u sin v, cos v) 0<u<2pi, 0<v<pi I have to find a normal vector to that surface. Homework Equations The Attempt at a Solution So tangent vectors can be Tu = (dx/du, dy/du, dz/du) and Tv =...

Hello, I understand the tangential shear stresses (or forces) acting on a fluid element due to friction between moving fluid layers, but I can't imagine how viscosity might cause a normal force (on a fluid element)...explain please!

Hi all! My question is the following. Suppose we have two normal topological spaces X and Y and we have a continuous map from a closed subset A of X to Y. Then we can construct another topological space by "glueing together" X and Y at A and f(A). By taking the quotient space of the disjoint...

Hi Physics Forum! I hope this is the right section... I couldn't find a section on statistics. This is a rather easy question but I can't seem to get the answer that the answer key says! Average Life expectancy μ=72 standard Deviation ( in years ) δ=5 The question: Recent studies have...

Homework Statement Find average value of Normal Acceleration from the information given. (See the picture) Homework Equations a^{→}_{ave}= Δv^{→}/Δt a_{t}=Δv/Δt The Attempt at a Solution I took the difference of the given angles in radians and divided it twice by Δt and get...

TITLE: Normal distributions (sorry) Question 1: Working: Now the answer for sigma i got correct, but μ i got incorrect for some reason. Could anyone explain where I've gone wrong for μ? Question 2: Workings: All i need help is with part c and d: for c) i done 1 - 0.6463 to get the...

Homework Statement A person who normally weighs 200 lbs is standing on a scale inside of an elevator. The elevator is moving downwards at a constant speed of 7.0 m/s and then begins to slow down at a rate of 4.9 m/s^2. Before the elevator begins to decelerate, the reading of the scale is...

Homework Statement Find the Jordan form and use it to find the matrix exponential. Homework Equations The Attempt at a Solution Let A =\begin{bmatrix} -3 &-1 &-1 &-1 \\ -1 & -3 & 1 & 1 \\ 1 & -1 & -5 & -1 \\ 1 & -1 & -1 & -5 \end{bmatrix}...

Need help calculating friction and normal force for "Measuring Friction" Lab Hey guys, I'm not great at physics and have a lot of work ahead of me so I could use some help. The lab setup is a wooden block sliding on a wooden surface. There is a weight attached to the block by a string that's...

Suppose I know that the diastolic blood pressure of my 30 patients is normally distributed with the same mean and standard deviation. Then the odds of one patient having a diastolic blood pressure is x higher than the others is the probability that the observed value of a normally distributed...

Homework Statement Prove that if p is a prime and G is a group of order p^a for some a in Z+, then every subgroup of index p is normal in G. Homework Equations We know the order of H is p^(a-1). H is a maximal subgroup, if that matters. The Attempt at a Solution Suppose H≤G and...

Homework Statement This is a two part problem A) Find a vector normal to the plane at (2,1,7) B) Find a vector normal to the plane tangent to the paraboloid at (2,1,7) Homework Equations Plane: z = x + y +4 Paraboloid: z = x^2 +3y^2 The Attempt at a Solution I'm not sure where...

Homework Statement Prove: If H is a subgroup with finite index in G Then there is a normal subgroup K of G such that K is a subgroup of H and K has index less than n! in G. Homework Equations Note: |G:H| represents the index of H in G |G:H| is the number of left cosets of H in G, ie...

Homework Statement If t = pi/2, then that would equal 2, but they don't say that t = pi/2 so how do they get 2? Maybe since it's circular motion t = pi, that would work too, but I want to be sure before i move on.

Normal distribution modified by "potential" For a random process the distribution if described by a gaussian distribution. But if the process has components that throw off the normal distribution, can any distribution be described by a gaussian distribution with another function, call it a...

Homework Statement Question: "Find the unit tangent, normal and binormal vectors T, N, B, and the curvature of the curve x = 4t, y = -3t^2, z = -4t^3 at t = 1." Answer: T = 0.285714285714286 i - 0.428571428571429 j - 0.857142857142857 k N = -0.75644794981871 i + 0.448265451744421 -...

Why is it that the normal force always point perpendicular to the plane? If I imagine the ground as made up of a bunch of particles I find it hard to see, why they should necessarily direct their forces perpendicular to the plane. Consider as a classical example a box sliding down a slope. The...

Just to help my understanding... 1) Can you have an abelian subgroup of a group which isn't normal? 2) Can you have a normal subgroup which isn't abelian? Cheers!

Homework Statement If I have a time series model x_1 = my + epsilon_1 x_i = my + a(x_{i-1} - my) + epsilon_i epsilon_i are iid standard normal. Can I then say that y = a_1 x_1+a_2 x_2 + ... a_n x_n is multi normal? The Attempt at a Solution All the x-es are normal...