Distribution Definition and 1000 Threads

1. Individual students’ scores on a national test have a normal distribution with a mean of 18.5 and a standard deviation of 7.8. At a Trade School, 84 students took the test. If the scores at this school have the same distribution as national scores, what is the mean, standard deviation and...

Greeting! My problem is to understand the flux of power inside this gearbox for example I can´t understand why the power in load 2 and load 1 are not equal to the power of the motor (suppose 100% efficiency). if this gearbox was an energy circuit (how to know that the energy is transmitted and...

I attached a Jpeg with my attempted solution but I´m not sure if I´m on the right way... I hope for a correction in my calculations

Please excuse me for posting in this group.l There seems to be little activity in the statistics group and i might get no response. For this example, lambda, is the average of dogs per 100 square miles = 0.05. if I wanted the probability of 2 dogs in 100 square miles I would calculate.. P(x=2)...

Hello! I am trying to solve this exercise of the electric field, but it comes out changed sign and I don't know why. Statement: On a straight line of length ##L=60\, \textrm{cm}## a charge ##Q=3,0\, \mu \textrm{C}## is uniformly distributed. Calculate the force this linear distribution makes...

Hi. I have found the answer to a and c (I don't know whether it is correct) but I do not know what I should find in question b. Is my method correct and how should I solve part b? Thank you for your help!

Hi, Please could someone explain in detail the arrangements of transmission cables in a UK pylon? In the image below there seems to be 3 sets of two wires on each side. As I understand it UK power stations produce 3-phase electricity so does each side come from two power stations? So this pylon...

Hi, I am not sure whether this is the right forum to post this. Please let me know if I should move and will do so. Overall question: Does the 'volatility' (i.e. standard deviation of the log returns) follow any sort of statistical distribution - maybe normal or log-normal? Background/...

In this question it is given that the sphere which is conducting is initially given a charge q then due to nonuniform mechanical strength and due to electrostatic force it creates a Small hemispherical bulge on its surface? okay my doubt is Let me define a term σ where σ is surface density...

We assume incident waves to be: y(1)=y(o)sin(wt) y(2)=3y(o)sin(wt+Φ) As Intensity~(Amplitude)^2 We get y(2)=3y(1) This gives us I(2)=9I(1) We assume I(1)=I(o) & I(2)=9I(o) Resultant Wave Intensity I=I(1)+I(2) +2√(I(1)*I(2))*cosΦ ----> I(o) + 9I(o) + 6I(o)cosΦ (We can take cos of this...

Gauss' law: $$\iint_{\partial A}\vec E\cdot d\vec A=\frac{Q}{\epsilon_0}$$ Suppose we have a unevenly charged non-conducting spherical shell, in which a Gaussian surface is placed. In this case, is the electrical field on A 0, given that there is no charge inside A? I came up with this example...

Hi, I am a math noob and need to understand what is the best mathematical formula for fair distribution. The problem statement is as follows: We choose 2 numbers at a given time to distribute donations at a particular instance in time (The numbers from 1-6500 represent community members...

Hello for everyone. I have a question according the field distribution in the semiconductor while the field effect. According to logic, the field is scrreened due to the field of the polarized carriers like electrons and holes. I know about the Debiye length. And that the field on the infinity...

v=50m/s ∆Pg= -981Pa ∆𝑝𝑑 =490Pa c=1m 𝜌 = 1,225 kg m3 𝐹3 = ∫ ∆𝑝3 ∙ 1 ∙ 𝑑𝑥 𝑐 2 0 = ∆𝑝𝑔 ∫ 2∆𝑝𝑑 𝑐 𝑥𝑑𝑥 𝑐 2 0 = 2∆𝑝𝑑 𝑐 ∙ ( 𝑥 2 2 ) c⁄2 | 0 = 2∆𝑝𝑑 𝑐 ∙ 𝑐 2 4 ∙ 2 = ∆𝑝𝑑 ∙ 𝑐 4 = 490,5 ∙ 1 4 = 122,625 N Lift per unit of span = (F1) + (F2) +F3 + F4= 490.5+245.25+122,25+122,625=981N :confused: Pressure...

Hello, in one of tasks of my liquid scintillation lab is to determine the average energy. You can see from the graph that data I obtained is similar to this one that I have a excel sheet data. X-axis is for beta particle energy from 0-156keV while y-axis counts of the particles. So according to...

Hi, I'm reading Chapter 2-II of of Duderstadt & Hamilton's "Nuclear Reactor analysis". In the section "Differential scattering cross sections with upscattering" it is discussed the situation in which neutrons suffers elastic scattering collisions in a hydrogen gas at finite temperature T and the...

I started by trying to write a normal distribution function for losing and not sure if that is possible.

What is the meaning of this proof? What is the meaning of last statement of this proof? How to prove lemma (7.1)? or How to answer problem 1 given below?

This is the problem; Find my working to solution below; find mark scheme solution below; I seek any other approach ( shorter way of doing it) will be appreciated...

Hey guys, I've about a week left to submit my final paper for my trade degree in transportation. The paper is about an analysis of potential implementation of an electric car for direct deliveries in my area where I live. In part of it, I try to analyze how many possible trips a car like...

1)In my book , there is a definition of fermi energy as topmost filled level in the ground state of an N electron system. This definition holds only for absolute zero,right? If it is not absolute zero,fermi energy is the energy at which the probability of a state being occupied is 50 percent...

I`m sorry if this seems too obvious, just trying to clarify something. When Fermi-Dirac distribution is equal to zero , can we assume it is the state of the highest energy? (Because the propability of occupation is zero)

The limit itself is pretty easy to calculate ##lim_{T->0} \ lim_{\mu->\epsilon_F} \ (e^{\frac{(\epsilon_F - \mu)}{kT}}+1)^{-1} = \frac{1}{2}## But I'm very confused about changing ##\epsilon_\vec{k}## to ##\epsilon_F##. Why do we do this?

Hello Can anyone explain what formula (or parameters) was used to create the exponential Boltzmann distribution in fig 2a of this document? http://image.sciencenet.cn/olddata/kexue.com.cn/upload/blog/file/2009/5/20095251352697121.pdf I figure it must be something like y=e^(ln(600)-b*x) for some b?

A random variable is distributed uniformly over a circle of radius R. What does the cdf ##F(x,y)## look like as a function of the Cartesian coordinates? The pdf can be expressed as ##f(x,y)=\frac{\delta(\sqrt{x^2+y^2}-R)}{2\pi R}##, where ##\delta## is Dirac delta function. Integration is...

All I can say is that where the charge density on surface is higher, we will have a stronger electric field compared to areas where charge density is lower since more charges means greater electrical force on a test charge placed very close to the surface. Also, the potential on pointed areas...

Hi, I cannot figure out how they got Table 2.1. For example, how come when x=1, F_X(x)=1/2? Could you please help me with it? Hi-resolution copy of the image: https://imagizer.imageshack.com/img923/2951/w9yTCQ.jpg

This doubt is confusing to me. I know it's something to do with conductors and insulators, but cannot explain. Conductors have mobile/free electrons unlike insulators. Having free electrons doesn't seem to explain this difference of charge distributions.

So just by by using the definition of the partition function... $$ Z = \sum_i e^{ \frac {-E_i} {k_BT} } = e^{ \frac {-0} {k_BT} } + e^{ \frac {-\epsilon} {k_BT} } = 1 + e^{ \frac {-\epsilon} {k_BT} } $$ And then, a result we obtained in class by using the Boltzmann H factor to solve for ##S##...

Hi, I found this question online and made an attempt and would be keen to see whether I am thinking about it in the right manner? Question: Find the probability of two line segment intersecting with each other. The end points of lines are informally sampled from an uniform distribution...

Hi, I was attempting the following question and just wanted to check whether my working was correct: Question: A bag has three coins in it which are visually indistinguishable, but when flipped, one coin has a 10% chance of coming up heads, another as a 30% chance of coming up heads, and the...

Good Day : i reached the page 40 of Ashcroft Mermin book and after the equation 2.38 there is this expression of E(a,N) which is equal to Helmoltez Free energy F = U - TS , how this two terms F , E are related ? anyone can provide adequate explanation , and few useful references Best...

The probability that the lifespan of an insect of this species lies between 55 and 60 hours is represented by the shaded area in the following diagram.\\ Write down the values of a and b. $a=\dfrac{2}{4.4}= 0.455 b=\dfrac{3}{4.4}=0.682]$ ok this was a key to a test question from 2013 but mostly...

Hi all, first time on this forum. I know this may sound like a stupid question, but how does the magnetic field distribute? I am working on FEMM and i am analysing magnetic losses on steel ducts. I was checking the flux density and the magnetic field distributions and i was surprised when i...

The below comment by @vanhees71 is an interesting one and I would be interested in exploring its implications. I am inclined to think that we can draw certain inferences about nature based on how we interpret the probability function and what it tells us about the elements of reality of the...

$\newcommand{\szdp}[1]{\!\left(#1\right)} \newcommand{\szdb}[1]{\!\left[#1\right]}$ Problem Statement: A survey of voter sentiment was conducted in four midcity political wards to compare the fraction of voters favoring candidate $A.$ Random samples of $200$ voters were polled in each of the...

$\newcommand{\szdp}[1]{\!\left(#1\right)} \newcommand{\szdb}[1]{\!\left[#1\right]}$ Problem Statement: Let $S_1^2$ and $S_2^2$ denote, respectively, the variances of independent random samples of sizes $n$ and $m$ selected from normal distributions with means $\mu_1$ and $\mu_2$ and common...

There are two questions in the photo. I have attempted the solution (attached below) and I would be highly obliged if someone would verify the same. Edit- Sorry the images of the solution have uploaded in the wrong order. 5th and 1st Image comprise of both parts of Q1 while the remaining of Q2.

The equation below allows us to calculate the potential energy of a continuous distribution of electric charge. $$U=\frac {\epsilon_0} 2 \iiint\limits_\text{Entire electric field}\vec E^2\,dV$$ In my textbook, the author states $$U=\frac 1 {8\pi\epsilon_0}\iiint\limits_\text{Entire electric...

Hello, When you have a beta decay you get the typical continuos spectrum representing counts against the kinetic energy of the electron. But what's the shape and how I get the spectrum of the kinetic energy of the neutrinos? Thanks

I have a set of data (representing the strength distribution of samples), and I would like to fit a normal-Weibull grafted distribution. To the left of a specified graft point, the distribution is Weibull, and to the right it's normal. At the graft point, the value and the first derivative are...

Could anyone suggest a simple video showing the Maxwell-Boltzmann distribution under the influence of a gravitational field? I trying to show a flat earther idiot how pressure gradients arise in a simple manner. Thank you all. DF

We know that Dirac Delta is not a function. However, I just talk about the numerical version of it that we use every day. We can simply represent the Dirac delta function as a limiting case of Gaussian distribution when the width of the distribution ##\sigma->0##. $$ \delta(x - \mu) =...

I am thinking about how an electric field has energy associated with it. If a single electron exists alone in a remote vaccuum, I believe it has it's own electric field surrounding it, and that this field has an energy content associated with it. My question is; does this electric field store...

I am not that super expert of statistics, so feel free to shift my formulation of the problem into the right one.First, for a physicist, the basic formulation of the problem. Let us say that you have a gravitational field and you have a fully symmetric problem on a flat world without other...

Hi All, Am new here came particularly hoping for some guidance I need to calculate theoretically, how different types of particles (shown below) distribute in a granular convection Condition: Large surface or open surface Types of particles: 1) Low volume, Low density particle 2) High...

I have an expression of Matter Angular power spectrum which can be computed numerically by a simple rectangular integration method (see below). I make appear in this expression the spectroscopic bias ##b_{s p}^{2}## and the Cosmic variance ##N^{C}##. ## \begin{aligned}...

a) Let X = distance walked on Friday and Y = distance walked on Saturday X ~ N (12, 0.192) and Y ~ N (10, 0.52) Let A = Y - X → A ~ N (-2 , 0.2861) P(Y > X) = P(Y - X > 0) = P(A > 0) = 9.2 x 10-5 But the answer key is 0.026 Where is my mistake? Thanks

Is it correct to say that $$\int e^{-i(k+k’)x}\,\mathrm{d}x$$ is proportional to ##\delta(k+k’)##?

I am not really sure what the reason is but my argument would be if normal distribution is appropriate, then almost all the score will fall in the range of μ - 3σ to μ + 3σ For this case, the range of μ - 3σ to μ + 3σ is 26.6 to 118.4 and all the score is unlikely to be within the range. I...