Normal Definition and 1000 Threads

Homework Statement If A,B and C are normal subgroups of G where B\subseteqA show that A\bigcapBC=B(A\bigcapC) Homework Equations The Attempt at a Solution Let x\inA\bigcapBC.then x\inA and x\inBC Now as B\subseteqA thus BA=A.thus left side is BA\bigcapBC Dont know how to proceed.

Hi - I have a quick question. I understand that the sum of two normal distributions is a normal distribution. Now let's say I have the z-score from one normal distribution and the z-score of another set of data that is also normally distributed and a third and a fourth etc. I just want...

Hi, I have a dataset of a random variable whose probability density function can be fitted/modelled as a sum of N probability density functions of normal distributions: F_X(x) = p(\mu_1,\sigma_1^2)+p(\mu_2,\sigma_2^2)+\ldots+p({\mu}_x,\sigma_x^2) I am interested in a fitting method can...

Show that if X is a normally distributed random variable with parameters mu and σ2, then then show that for each real number x we have: фX(x)=ф[(x-m)/σ] I have really hard time. Any possible hint is greatly appreciated.

Quick question on bivariate normal distribution please: I know for a bivariate normal distribution, the two variables are marginally normal and all the conditional distributions are also normal. Is the reverse true? i.e. if you have two random variables that are marginally normal...

Homework Statement Given in uploaded file Homework Equations σallow=\frac{P}{A} τallow=\frac{V}{A} The Attempt at a Solution Given in uploaded file Answers are d=16mm, h=10mm I tried using methods used in previous questions but it didn't work out for me here, if anyone could...

I'm on the last chapter of a 1200 page calc book, I'm really psyched. Homework Statement The Attempt at a Solution The method I learned for finding the unit normal of a vector field, n, is take the derivative of the equation and divide that by the magnitude of the...

Hey, I need help with the following question in microeconomics: A consumer lives in a world of two goods: computers and money. Let x be the number of computers,the consumer can buy. x\epsilon [0,1,2,3] The consumer has the following preference relation: If the consumer has money and no...

Am I right? Thank you!Problem: A cereal brand of cereal claims that the mean number of raisins in each box is 80 with a standard deviation of 6. If the raisins are normally distributed, what are the chances that an arbitrary box has 1) fewer than 70 raisins and 2) more than 90 raisins. What...

Two buckets of nails are hung one above the other and are pulled up to a roof by a rope. Each bucket has a mass of 5.0kg. The tension in the rope connecting the buckets is 60 N. Calculate the acceleration of the buckets. So here's what I did: mt= ma + mb (m which is equal to mass) mt=...

good day! i need to prove that the alternating group An is a normal subgroup of symmetric group, Sn, and i just want to know if my proving is correct. we know that normal subgroup is subgroup where the right and left cosets coincides. but i got this equivalent definition of normal group from...

I have a list of bearings that I want to convert. The normal degrees circle is oriented with 0 to 360 going counter clockwise. I have degrees calculations that require this. I have a set of data from bearings from an aircraft where I need to convert those bearings to normal degrees bearings. As...

Homework Statement Vector field ##\vec F= 4x \hat i+4y \hat j +3 \hat k## Let S be the open surface above the xy-plane defined by ##z=4-x^2-y^2## a. Evaluate normal outward flux of F through S. b. Use Stokes' theorem to evaluate the normal outward flux of ##∇ \times \vec F## through S. c...

Every semester, whenever I begin to learn a new subject, that is, a more advanced class of the previous subject (i.e. algebra -> pre-calc -> calc -> diff eq, etc.) I forget a lot of the stuff I learned in the previous class when I'm learning the new content and constantly have to review all the...

Given the function: w=\sqrt[3]{(z-5)(z+5)} which is fully-ramified at both the finite singular points and at infinity, how does one create the normal Riemann surface for this function? It's a torus but I do not understand how to map a triple covering onto the torus so that it's fully-ramifed...

H=A3= {(1),(1 2 3),(1 3 2)} and G=S3 ={ (1),(1 2 3),(1 3 2),(1 2 ),(1 3),(1 2 3) } Is H is normal subgroup of G ? I try g=(1 2 3 ) for gH=Hg but gH≠Hg for all g ε G.In this situation,H is normal subgroup pf G?

Let r and a each be a position vector of a point on a plane. Let n be the normal to the plane. The normal equation of the plane would be: n.(r-a) = 0 r.n = a.n My question is, the equation doesn't really 'describe' a plane...so what's the purpose?

I have to compare measurements in a normal distribution with a theoretical gauss curve on "probability paper" (the y-axis has percent). Does anyone know any online guide/ information? thanks, have wasted the last three hours on this

According to the Snell's Law refractive index n21= sin i/sin r, but when we use this equation while having a incident light normal to the surface of lens or any other refracting surface it becomes 0/0. So how can we define Snell's law in this situation?

We're given x^2+2*y^2=1. so x^2=1-2y^2 now using distance formula d^2=x^2+y^2 since x^2=1-2y^2, substituting it in the distance formula we get: d^2=1-2y^2+y^2=1-y^2; differentiating and then setting the eq to 0 we get; 0=-4y or y=0. now x^2=1-2y^2=1 so x=+-1 so point having...

1. A 5 kg board is arranged between 2 sawhorses (at right). If the board is in static equilibrium, what is the normal force on the board from sawhorse 2. Link for the picture the question is referring to. h.ttp://i.imgur.com/nBC6A.jpg a. F2,normal = 0 N b. F2,normal = 49.0 N c...

Homework Statement Consider a 2D spacetime where space is a circle of radius R and time has the usual description as a line. Thus spacetime can be pictured as a cylinder of radius R with time running vertically. Take the metric of this spacetime to be ds^{2}=-dt^{2}+R^{2}d\phi^{2} in the...

Homework Statement Light incident from air strikes a diamond at 30° a) At what angle to the normal a is the light reflected back into air? b) At what angle to the normal a is the light refracted inside the diamond? c) At what angle to the normal b is the light incident on the back...

Homework Statement Consider z = -3x - y + 11 Find a unit vector perpendicular to the plane, and find a vector parallel to the plane. Homework Equations The Attempt at a Solution 1.) 0 = -3x - y + 11 - z -11 = - 3x - y - z Perpendicular vector is then: -3i -j -k...

I bought a ravpower brand laptop power adapter half year ago,it works well before,but this week i find it will become very hot,I don't know why.But I am thinking maybe it is relative with the time of using or the voltage?Or some other problem?Sometimes I play games for all day and I have a bad...

Homework Statement Consider the subset H = {0,3} of the group Z6. (i) Prove that H is a normal subgroup of Z6. (ii) Prove that Z6/H is isomorphic to Z3. (Give an explicit isomorphism) Homework Equations In order to be a subgroup H must be closed under +6, have an identity, and have an...

Hi all, just a small question: why does a normal metal junction does not show a josephson like current when inserted in a squid setup? I guess it is something related to the coherence of the ground state...

Hi, why does the energy of the system equals the sum of the energy of the modes? The book I'm reading only states it, it doesn't prove it.

Hi, Can someone here help me understand how to illustrate maps of analytically-continuous paths over algebraic functions onto their normal Riemann surfaces? For example, consider w=\sqrt{(z-5)(z+5)} and it's normal Riemann surfaces which is a double covering of the complex plane onto a single...

Homework Statement An infinite cylinder with radius 1 is aligned with axis Y, A point light source with intensity 1 is located at (2,2,10) An observer is located at (3,1,4). He is looking in the direction of the origin of the coordinate system. What are the coordinates of the point on the...

Homework Statement Homework Equations σ=P/A σ=My/I τ=VQ/ItThe Attempt at a Solution I'm on part C, pretty sure I have A and B, so I'm using a W18x46 Beam. I have drawn shear and moment diagrams. I just want to be clear on what part C is asking... I'm assuming this point is at the end of...

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...

Homework Statement Let G be a group and H normal with G. Prove that if |H| = 2, then H is a subgroup of Z(G). Homework Equations The Attempt at a Solution Since H is a subgroup, it must contain the identity, call it e. Call the non-identity element of H h. Thus, H = {h, e}. Since H contains...

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...

So I'm kinda new to Physics Forums but I've been using threads as guides for about a year now. Basically, I'm hardcore studying for my Calc III exam (the final is in a few weeks) and I came across an interesting lapse in my understanding (well many in fact, but one in particular). First of...

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 The signal s(t) is a deterministic signal with the finite duration (0,Ts) and the energy Es=∫s2(t)dt. In the following system, n(t) is a normal noise with the mean zero and the power spectral density Gn(f)=η/2. Show that no(Ts) has a normal distribution with the mean zero...

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...