Variable Definition and 1000 Threads

Hey! :o For a random variable $X$ the skewness is defined by \begin{equation*}\eta (X):=E\left (\left (\frac{X-\mu }{\sigma}\right )^3\right )\end{equation*} where $E(X)=\mu$ and $\text{Var}(X)=\sigma^2$. I want to show that \begin{equation*}\eta...

Homework Statement The Cepheid variable star l Carinae pulsates with a period of about 36 days. During each pulsation, the star becomes about twice as bright and its radius grows by about 25%. (a) In its smaller state, the star has a surface temperature of about 5100 K. Treating the star as a...

I want to integrate this: \int_0^∞ re^{-\frac{1}{2σ^2} (r-iσ^2q)^2} \, dr. If I change the variable r into t with this relation:r-iσ^2q=t, then the integral becomes\int_{-iσ^2q}^∞ (t+iσ^2q)e^{-\frac{1}{2σ^2} t^2} \, dt so it seems I cannot use the famous gaussian integral formula. But I got the...

I got my education out of the American continent, yet currently I live in Canada and my son goes to school here (5th grade + some additional math training) What puzzles me is that currently he may write things like $$5\times-1$$ meaning ##5\cdot(-1)##, which I can only read as ##5x-1## (i.e...

Hello, I know that the derivative of Dirac-delta function (##\delta'(x-x') = \frac{d}{dx} (\delta(x-x')))## does the following: ##\int_{-\infty}^{\infty}\psi(x')*\delta'(x-x') dx' = \frac{d\psi(x)}{dx}## it is easy to visualize how the delta function and the function ##\psi(x')## interact along...

Homework Statement A massless string of length 2l connects two hockey pucks that lie on frictionless ice. Aconstant horizontal force F is applied to the midpoint of the string, perpendicular to it (see right figure). How much kinetic energy is lost when the pucks collide, assuming they stick...

Homework Statement Calculate the geometric phase change when the infinite square well expands adiabatically from width w1 to w2.Homework Equations Geometric phase: \gamma_n(t) = i \int_{R_i}^{R_f} \Bigg< \psi_n \Bigg | \frac{\partial \psi_n}{\partial R} \Bigg > dR Infinite square well wave...

So, I am doing my undergraduate research project in Quantum Cryptography, and I have some confusion in a few areas, especially in the topic of continuous variable quantum key distribution. From what I understand, Discrete Variable - Single photon. That is, for example, the BB84 protocol. Bob...

Can someone help with the issue/problem of placing a superscript before a variable or expression ... as Just and Weese do in their book on Set Theory ... in the expression for a Cartesian Product as follows: Hope that someone can help ... Peter

Is the object of an experiment a variable?

Can all equations with a single variable be solved? 5 = (x)/(1+x^7) How can something like this be solved for example. Sometimes I have equations with one variable and I can’t see any way to solve them with the knowledge of math that I currently have. Is it just that a higher level of math is...

The solution of 1D diffusion equation on a half line (semi infinite) can be found with the help of Fourier Cosine Transform. Equation 3 is the https://ibb.co/ctF8Fw figure is the solution of 1D diffusion equation (eq:1). I want to write a code for this equation in MATLAB/Python but I don't...

I am trying to reconcile apparent differences between the definitions of the derivative of a vector-valued function f: U \rightarrow \mathbb{R}^n (where U \subset \mathbb{R}^m ) of a vector variable from two textbooks ... The textbooks are as follows: Andrew Browder: "Mathematical Analysis...

Homework Statement X is a Poisson Random Variable with rate of 1 per hour, following the Poisson arrival process a. Find the probability of no arrivals during a 10 hour interval b. Find the probability of X > 10 arrivals in 2 hours c. Find the average interarrival time. d. For an interval of 2...

Homework Statement X is a geometric random variable with p = 0.1. Find: ##a. F_X(5)## ##b. Pr(5 < X \leq 11)## ##c. Pr(X=7|5<X\leq11)## ##d. E(X|3<X\leq11)## ##e. E(X^2|3<X\leq11)## ##f. Var(X|3<X\leq11)##Homework EquationsThe Attempt at a Solution Can someone check my work and help me? a...

Homework Statement See attached image (See below) Homework Equations Differential equations. And a combination of discrete & continuous distributions The Attempt at a Solution The Continous Distribution Function (CDF) is given in the question. So I differentiated it with respect to x...

Hello, I would like to create few functions in loop by Table (not ordinary change a parameter, but different numerical solution of problem). The names should differ by "number"of the step, let's say "i", in the name. I.e. I would like to get set of function f"i"={f1=Interpolation[data]...

I am installing an installing an open source software -on Ubuntu 16.04- by reading its 'http://ftp://ftp.chesapeakebay.net/../Modeling/Phase5/community/P53/README.txt' file. At certain point (point 3b in the link) the guideline requires me to run a .csh file located in a certain directory in...

I am new to quantum mechanics and I have recently been reading Shankar's book. It was all good until I reached the idea of representing functions of continouis variable as kets for example |f(x)>. The book just scraped off the definition of inner product in the discrete space case and refined it...

Homework Statement I have two equations and I want to write them in terms of |0> and |1> as a function of |b> and |d> note: |i> is a kent or a qubit Homework Equations |b> = cosα |0> + eiβ sinα |1> |b> = sinα |0> + e-iβ cosα |1> The Attempt at a Solution

Dear all, We were trying to solve the following question but did not quite understand what to do. The question is as follows: The reconstructed invariant mass is usually described by a Gaussian (or Normal) distribution. However, the resolution σ (the width of the distribution) is found to...

This process and mechanism is very difficult to explain via the computer and even during presentations many people simply do not grasp the concept so I am trying my best to explain it easily and ask my questions as best as I can so that you guys understand me. I really need help with these few...

Hi, I need to solve Laplace equation ## \nabla ^2 \Phi(z,r)=0## in cylindrical coordinates in the domain ## r_1<r<r_2 ##, ## 0<z<L ##. The boundary conditions are: ## \left\{ \begin{aligned} &\Phi(0,r)=V_B \\ &\Phi(L,r)=V_P \\ & -{C^{'}}_{ox} \Phi(x,r_2)=C_0 \frac{\partial \Phi(x,r)}{\partial...

Homework Statement Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values. x1−2x2+2x3 = −1...

I don't understand what they are doing here. They start with the mgf for the binomial which I understand. But what is ##E[e^{tX}]##? The average of the binomial mgf? And finally why does this explain that X is equally likely to take on any of the values 0,1,..,n?

##\displaystyle \frac{\partial u(x,t)}{\partial t}-p(x) \frac{\partial^2 u(x)}{\partial x^2}-\frac{\partial p(x)}{\partial x}\frac{\partial u(x)}{\partial x}=f(x,t)##. With periodic boundary conditions: ##u(x,t)=u(x+2\pi,t)##. The right hand side is also a periodic function of space, and it can...

Hey! :o Can the minimum of the average variable cost function be negative? (Wondering) Suppose we have the cost function $K(x)=x^3-9x^2+11x+100$. The variable cost function is then $K_v(x)=x^3-9x^2+11x$. The average variable cost is $k_v(x)=\frac{K_v(x)}{x}=\frac{x^3-9x^2+11x}{x}=x^2-9x+11$...

Hello all! I usually don't like to ask for help... But this is the first week of courses and I'm already stumped on a homework question... 1. Homework Statement So the question states: Find the work by the force F = x^i + xy^j. If the object starts from the origin (0,0), moves along the...

Homework Statement A CD case slides along a floor in the positive direction of an x-axis while an applied force Fa acts on the case. The force is directed along the x-axis and has the x component Fax = 7.0x – 2.0x^2, with x in meters and Fax in Newtons. The case starts at rest at the position x...

Ok so this week I was studying aerodynamic differences between a "Fat Man" bomb which was dropped on Nagasaki and the Aim 120c Air to Air Missile. What intrigued me with nuclear weapons was the "Variable Yield", SO I did some research to see how it works . I couldn't mind much on how to adjust a...

With E a,b = ( dλ ( a,a' b,b' λ) Suppose λ depends independently/locally on detector setting choices at A and B. For example suppose there are 360 detector settings at A and 360 at B , corresponding to 360 particle/detector interactions/outcomes at A = ± 1 and also at B = ± 1. Then as θ =...

Hi All, I have many Likert variables regarding a single item issue. Specifically, I am dealing with several measures of IT Dept Quality, like % of budget devoted to IT department, Number of External Audits, etc ; each is measured on a Likert scale. I ultimately want to regress EDIT against...

Hello, I have an equation of the form: ##\partial_t f(x,t)+a\partial_x^2 f(x,t)+g(x)\partial_xf(x,t)=0 ## (In my particular case ##g(x)=kx## with ##k>0## and ##a=2k=2g'(x)##) I'd like to know if there is some general technique that i can use to solve my problem (for example: in the first...

Hi PF! I am trying to plot a difficult implicit function, but for ease let's pretend that function is ##y^5\sqrt{1-x}+yx+1 = 0##. I want to plot ##Re(y)## as a function of ##x:x\in[0,2]##. I am using MATLAB. Do you think the best way to plot this is to assign ##x## a value in the domain, use...

So what if my response variable, y, is say a scale. For example, ranking, something like 1-10. How would I transform the response to make linear regression work?

Homework Statement Homework Equations $$ \log_{x} a \ means \ 10^x = a $$ $$ \log_{x} {a^n} = n \log_{x}{a} $$ The Attempt at a Solution $$ \log_{10} {ax} \log_{10}{bx} + 1 = 0 $$ $$ \ means \log_{10} {ax} = 1 \log_{10}{bx} = -1 \ or \ vice \ versa $$ $$ \ for \log_{10} {ax} = 1 \ so \ ax...

A static E Field and vice Versa? Or a time variable field created also another time variable Field?

I'm trying to integrate a simple function (x*y) using the Romberg method. Question 1: I want to integrate only x and maintain the argument y present in the rest of calculation, like a global variable. In fortran 77 I would use common. Question 2: How to integrate using arguments in the...

Hi. I have been trying for sometime to solve the following system of DEs analytically(Is it possible?) but no luck so far. $$x''(t)=-z(t)x'(t)-x(t)+y(t),$$ $$y'(t)=-z(t)y(t)+x^2(t)$$ $$z'(t)=-2z^2(t)-x(t)$$. With the initial conditions ##x(0)=1## , ##x'(0)=0## ,##y(0)=0## and ##z(0)=1##...

So I recently learned that Teslas use AC induction motors rather than DC motors. Now I always assumed that DC motors would be easier to control the speeds of vs. induction motors, so it surprised me that they used an induction motor in the Teslas. Now in my old days I had heard that induction...

So if I have a study where people are randomized within treatment sites do I always have to have the site indicator in the regression equation? This text(Homsler and Lemmeshow 2nd ed) says yes. Here is some context provided below. And here is the output for the multivariate equation after...

After going through the starting parts of Astrophysics, (and excuse me if I completely mess this up), that if the apparent brightness of the star decreases due to the loss in energy and contracts then expands again over a certain period. Then as the energy released has a mass equivalence, then...

I am trying to understand the fixed cost of a nuclear power plant relative to variable cost. By fixed cost I mean "cost that does not vary with the amount of the power outputted over a given time period." By variable cost I mean "cost items that vary with the amount of the power outputted...

Functions are pretty simple things , they just express a relationship between two different quantities How do i express this function in terms of y(x) = something ?

Homework Statement I have a task right now that requires me to calculate the energy savings that would be made by using a variable speed drive. Question: The factory process water distribution system consists of a 150mm cast iron ring main at a pressure of 5 bar (50m). The local water is...

I have recently been doing some work that involves long, messy manipulations with lots of geometric series. A typical such series, which would only be one of a number of such terms in a formula, is: $$ \sum_{t=h+1}^{T-h} \left(1-(1-\theta)^{T-t-h+1}\right) \\ $$ It's not difficult to simplify...

Hi, I want to be able to vary the amount of capacitance in a circuit, ideally I'd like to be able to turn a knob to tap a bank of capacitors, something like the attached picture.Is there some sort of switching or device available that anyone can think of which does this? Cheers

1. Homework Statement First, if you want to skip my explanation, I believe the error is somewhere in the last 15 lines of code or so. Heres some background on test cases: Use stating member variables to use a class that helps you convert a double number into english words. For example, if a...

I just have a couple of questions about how it can be zero probability. In case, you have a continuous cumulative probability distribution such that there is a derivative at each point not equal to zero. This means that every point as a different value than the other which means that every...

Homework Statement A set of eight numbers has a median of 19. a) What is the sum of the fourth and fifth data points b) What is the sum of the fourth and sixth data points (no answers available) Homework Equations (N+1)/2 -- Position of the median (N+1)/4 -- Position of Q1 3(N+1)/4 --...