Variable Definition and 1000 Threads

So I have X1 and X2 are iid standard normal. Then I have Y=X1^2+ X2^2 and Z=X1/(X1^2+x2^2) I'm supposed to find the distribution of Y and Z and then determine if they are independent. Clearly Y is chi squared with degrees of freedom 2. But I have no idea how to find the distribution of Z...

Homework Statement Solve the following: [/B] y'' = c2 / (x2 + c1*x) * y c1, c2 are constants, x is variableHomework Equations As above The Attempt at a Solution I have used the method of Frobenius and regular power series and obtained an infinite series on top of an infinite series, which is...

Is there a simple formula to find the amount of money in an account given a situation like this... You deposit x into the account Each year you get interest Year one the interest is 1% Year two the interest is 2% Year three the interest if 3% and so on Is it possible to get a simple general...

Homework Statement Let X denote a continuous random variable with probability density function f(x) = kx3/15 for 1≤X≤2. Determine the value of the constant k. Homework Equations I'm not sure if this is right but I think ∫kx3/15 dx=1 with the parameters being between 2 and 1, The Attempt at a...

Homework Statement If X is uniformly distributed over (0,1), find the PDF of Y = |X| and Z = e^X Focusing on the |X| one Homework Equations Derivative of CDF is the PDF The Attempt at a Solution So I start by writing down the CDF of X, Fx(x): 0 for x <0 x for 0 ≤ x ≤ 1 1 for x ≥ 1 And I...

Homework Statement Here's the problem with the solution provided: Homework Equations Fundamental Theorem of Calculus (FToC) The Attempt at a Solution So I understand everything up to where I need to take the derivative of the integral(s). Couple of things I know is that the derivative of...

Homework Statement Evaluate: I(y)= \int^{\frac{\pi}{2}}_{0} \frac{1}{y+cos(x)} \ dx if y > 1 Homework EquationsThe Attempt at a Solution I've never seen an integral like this before. I can see it has the form: \int^{a}_{b} f(x,y) dx I clearly can't treat it as one half of an exact...

Although the speed of light is constant in GR, within coordinate spacetime the speed of light varies. For example, light travels more slowly near a black hole than in remote space. The same is theoretically true of the speed of gravity. But is there any supporting empirical evidence?

Is this possible? It seems like it should be but, it's difficult to find an explicit relationship between a general function of one variable x (let's say we are only interested in functions that decay to zero as they go to plus or minus infinity) it seems like summing a bunch of gaussians of...

The title may seem dumb because increase in voltage but I wanted to have sort of like a transmission for an electric motor which again... increase in voltage which may make this idea unnecessary but I wanted to have a motor that was built like a cone within a cone so that you could slide the...

Homework Statement [/B] Use integration by substitution to evaluate the integral, I = \int^{x}_{x_{0}} (3 + 4t)^{\frac{5}{3}} dt Homework EquationsThe Attempt at a Solution I am confused by this question, and think that the limits on the integral might be a typo. Does it make sense for them...

Homework Statement A force F has components F sub x = axy-by^2, F sub y= -axy+bx^2 where a= 2N/m^2 & b=4N/m^2 Calculate the work done on an object of mass 4kg if it is moved on a closed path from (x,y) values of (0,1) to (4,1), to (4,3) to (0,3) and back to (0,1). all coordinates are in metres...

Homework Statement So I have a group lab for physics, but I need some alg/trig help isolating v for a derived equation. I've tried many times to to get v0 by itself but when I check the equation with the values that I have for each variable I always get the wrong answer. ∆y =...

How to prove: $\int_{0}^{\frac{\pi }{2}} {\frac{\sin \theta}{\sqrt{Z^2+(R+h \tan \theta)^2}} K[k(\theta)]}=\frac{\pi }{2\sqrt{R^2 + (h+Z)^2}} $ where \[ k(\theta)=\sqrt\frac{4Rh \tan \theta}{Z^2+(R+h \tan \theta)^2}\] and $ K[k(\theta)] $ is the complete elliptic integral of the first kind...

We have a r.v. X with p.d.f. = sqrt(θ/πx)*exp(-xθ) , x>0 and θ a positive parameter. We are required to show that 2 θX has a x^2 distribution with 1 d.f. and deduce that, if x_1,……,x_n are independent r.v. with this p.d.f., then 2θ∑_(i=1)^n▒x_ι has a chi-squared distribution with n...

Can anyone point me to some material on applying the Fourier transform to the case of an analytic function of one complex variable? I've tried to generalize it myself, but I want to see if I'm overlooking some important things. I've started by writing the analytic function with u + iv where u...

A 1.2 kg block is held against a spring of force constant 1.0 x 10^4 N/m, compressing it a distance of 0.15m. How fast is the block moving after it is released and the spring pushes it away?

Homework Statement I have no values at all, so it's just going to be the variables in the relevant equations. I need to define mu using those variables. A carousel is moving in a circle at velocity v and has a radius r. It is moving fast enough that each person with mass m is pinned against the...

I want to write a line of code at the top of my .nb and have Mathematica treat the specified variables as real only. I've tried using "Assumptions" and "Assuming", but it just won't work. I still get back answers where the entire expression is returned inside the Re[ ] command, like it is...

If one has a Bernoulli random variable W that is derived from a Variable T (Poisson λ), by the following rules W = (if T=0 then W=1 and if T>0 then W=0), I am having trouble finding the pf for W. Any suggestions about how to proceed forward?

So on my first course of Algebra in university I have been asked to find the image of the following function: f : Z x Z -> Z, f(x, y) = x2 - y2 In high school I worked only with single variable functions and I could have found the image by drawing its graph, using limits or using some specific...

Hello, I do a lot math and physics work, (predominantly advanced fundamental theories), and have consistently been hindered by a particular issue when it comes to a few of my defined functions. I feel like it would be a kind of "order of execution" issue with a simple solution, but though I've...

I am trying to display the input that I enter into the dialog box from "inputdlg" function into a text file. This is what I've so far: prompt={['What is your name?']}; title = 'Name Machine'; answer = inputdlg(prompt, title); name = answer{1}; fileID = fopen('NameMachineFive.txt', 'w')...

Homework Statement Given :  x+y+5z = 2   x+2y+7z = 1   2x−y+4z = a . a) Determine the value of a which will make the given system have many solutions. Explain your answer. b) Choose a value of a which will make the given system have NO solutions. Explain your answer. c) Is it possible...

ok so i realized my problem with c++ is that i don't really understand for loops. well it's not exactly the loop itself but i don't understand the loop variable [i]. what is for EXACTLY? why is it needed? why can't you just use the other variable you are using? why does this extra variable need...

I'm having trouble understanding the relationships between various variables at play in diffraction. Say you have diffraction with one slit, two slits, and a grating as shown below. So 1) The Amplitude of each peak is directly proportional to the intensity of the incoming waves. This makes...

Homework Statement A bag contains a large number of coins comprises of 1 cent and 5 cents coins in the ration of 1:3 find the man and variance of the values of coins.. i have attached the sample ans here. i don't understand why the value of '2' is used?? why not '5' ...for me '5' represent 5...

Hello! (Wave) If we have the following for loop: for (i=8^{n-1}; i<8^n; i+=1) (where $n$ is an integer) does $i$ take the values $8^{n-1}, 8^{n-1}+1, \dots, 8^n-1$, or am I wrong? (Thinking)

I would like to reopen a discussion on assertions made by David Mermin such as: “There is no conceivable way to assign such instruction sets to the particles from one run to the next that can account for the fact that in all runs taken together, without regard to how the switches are set, the...

Background: I am trying to write a program for Buckingham Pi Groups. I need to find a way to list all the input varialbes as different sets. For example if I have 4 variables [V D p u] and I want to distribute them 3 ways I get 4 sets. Number of Sets = Binomial(Number of Variables...

With a Poission random variable, we know that \(E[X] = var(X) = \lambda\). By definition of the variance, we can the second moment to be \[ var(x) = E[X^2] - E^2[X]\Rightarrow E[X^2] = var(X) + E^2[X] = \lambda(1 + \lambda). \] The characteristic equation for the Poisson distribution is...

Homework Statement Consider the diagram below. A 1000 kg block being suspended in equilibrium by cables c and a. Cable c is on a pulley which can vary the length of the cable. Write the constraints of equilibrium. Find the tension in each cable based on varying lengths of cable c between 1.2 m...

I'm looking at getting a motor to drive a micrometer. It's on an interferometer mirror for the curious. I'll need around 1RPM or so, but I want to be able to vary the speed, because I'm pretty unsure about how fast I'll need it to go for my experiment to work. I'm thinking a range of like 1/4 to...

Homework Statement evaluate the double integral of cosh(6x^2+10y^2) dxdy by making the change of variables x=rcos(theta)/sqrt(3) and y=rsin(theta)/sqrt(5) let D be the region enclosed by the ellipse 3x^2+5y^2=1 and the line x=0 where x>0. Homework EquationsThe Attempt at a Solution first I...

what is the purpose of a loop variable (i)? how is it useful?

The equation is: (appears while solving a trigonometric integral using residue theorem) 2Z2+iZ2-6Z+2-i =(2+i)Z2-6Z+(2-i) The roots are: Z1=(2-i) and Z2=(2-i)/5 I can't write the equation in factored form. If I simply write it like this: {z-(2-i)}{5z-(2-i)} It doesn't give the same...

The discrete random variable K has the following PMF: p(k) = { 1/6 if k=0 2/6 if k=1 3/6 if k=2 0 otherwise } Let Y = 1/(1+K), find the PMF of Y My attempt: So, I am really confused about what this is asking. I took...

I am not sure if this is supposed to go in the homework forum or not since it is more of an off physics topic so sorry if it is incorrect. I have a programming assignment for class and I am having a lot of trouble with a while loop. For this part of the program I have to prompt the user to...

Hello everyone. I've been struggling with how to deal or solve questions that include variable masses. Considering the method I usually try to solve with, it either gets me lost or just makes things complicated and doesn't work often to me. :P I was wondering if you guys could help me out...

I accidentally posted this to the "Calculus & Beyond" forum when I meant to post it to the physics forum. If someone can tell me how to move this post, I will get rid of it here! Homework Statement Consider a property, for example temperature θ, that is conserved during advection (i.e. Dθ/Dt =...

Hi, I want to solve the following diffusion equation: (d/dt) C(r,z,t)=D*∇^2 C(r,z,t) where C is the concentartion and D is the coefficient of diffusivity (constant) with initial condition C(r,z,0)=C0 (constant) and boundary condition dc/dr=0 at r=0; (dc/dz) at z=-L equal to (dc/dz)...

i don't even understand this... Given shipWeight in pounds, compute the cost to ship a package and assign to shipCost. Shipping involves a flat fee of 75 cents, plus 25 cents per pound. Declare and use a const named COST_PER_POUND. Sample program: #include <iostream> using namespace std; int...

How do I estimate the pdf from a random variable \(X\) where \(X = U_1 - U_2\) and \(U_i\) are uniform random variables? In the code below, I used unifrnd(-5, 5, 1000, 1) which generated a 1000x1 vector of uniform random number between -5 and 5. How do I estimate the PDF for X? rng; X =...

A motor boat of mass m moves on the surface of a lake at a speed0v. At the moment 0t= the engine is shut down. Assuming the resistance of water to be proportional to the speed of the boat, F=−rv, find a) the time interval after which the boat stops; b) the speed of the boat as a function of...

Homework Statement The wave function ψ(x)=Ae-b2x2/2 where A and b are real constants, is a normalized eigenfunction of the schrodinger eqn for a free particle of mass m and energy E. Then find the value of E Homework Equations The Attempt at a Solution Substituting the wave...

Homework Statement please refer to the question, i can't figure out which part i did wrongly. i 'd been looking at this repeatedly , yet i can't find my mistake. thanks for the help! the correct ans is below the question. where the c= 283/5700 , q = 179/5700 Homework Equations The...

For certain types of functions I have been using the term 'general form' as a way of stating that some function of some variable(s) is true for more than one value of the variable (usually an infinite number). Here is a simple example, 1=cos(2∏x) There have been (at times) where the use of...

How would someone go about writing a general expression for a function of a single variable and a constant? For example, if we have a function of two variables 'x' and 'y' we can use f(x,y). If we had a function of 'x' and the constant '∏' is it acceptable to write it as f(x,π)?

Homework Statement This isn't actually homework. I was messing around in my notebook trying something when I ended up writing something to the effect of this: dT = \frac{V^{2}}{R(1+α dT)}dQ R(1+α dT) dT = V^{2}dQ Where α and V are constants. Now, I'm fairly sure what I had done made...

Homework Statement Dear friends, let U and V independent variables that are both defined on [-∏, ∏] and are uniformly distributed. If x = cos(U + V) and y = sin(U-V), what is the area where the variables X and Y are defined? Homework Equations U + V = arccos(x) U - V = arcsin(y) For a test...