Variable Definition and 1000 Threads

Hi there. In the multivariate case it is proven that if X~Nm(U, S) and Y = a + CX where C is an invertible n x n matrix, and S is the covariance matrix then: Y ~ Nm(a + CU, CSC') I am trying to apply this proof to a similar problem. If we have X1...Xk with Xi ~ Nm(Ui, Si) where i = 1...k...

Homework Statement Given a random variable X with a known distribution (e.g. a beta distribution), find the distribution of f(X) = X^2 + X The Attempt at a Solution I've tried the normal approaches: the standard transformation theorem; conditioning on X; Laplace transformation, etc...

Homework Statement That's a graph of Force in Newtons (y axis) vs displacement in meters (x axis) for an object of mass 3.0kg that is moving along the x-axis and initially starts at rest. I am being asked to find the total work done on the object as it moves from x = 0 to x = 7...

Homework Statement A light bulb and a resistor are connected in series to a variable power supply. A student first connects a voltmeter and an ammeter to measure the current through and the voltage across the bulb, as shown in the left circuit. The student varies the power supply voltage and...

Homework Statement Compute the following sequence (show your work) (-2)n+3n ÷ (-2)n+1+3n+1 The Attempt at a Solution (-2)n+3n ÷ (-2)n(-2)+3n3n After this I don't know what to do. I know that if I can prove that something smaller than this for all n's converges to +∞, this will...

Can a variable star become a non variable one? Or viceversa, can a non variable, as it is (almost) the sun, become quickly (say few thousands of years) a variable one? Is there any record (e.g. in the geological records) which shows that the sun had once a very different luminosity? Has this...

Hello, I have a really tough time understanding this concept although this isn't anything more complex than a composition of functions. I have a done example from my book that I am trying to interpret. p_\xi (x)=\frac{1}{\pi} for an interval between [0,∏] The...

I have a system where a cable is pulled down with a load of 100-200 lb. I need a motor that resists this load with a force that can be programmed to be anywhere from 5-30 pounds. I don't want the motor to stop the downward motion, just to offset the magnitude of the force pulling down on the...

A water glass (10 cm diameter at the top, 6 cm diameter at the bottom, 20 cm in height) is being filled at a rate of 50 cm^3/min. Find the rate of change of the height of the water after 5 seconds. V=(∏* (h/3)) * (R^2 + r^2 +(R*r)) I've been messing around with this for a bit and made a...

Which of the following is an analytic function of the the complex variable z = x+iy in the domain lzl <2 ? (3+x-iy)^7 [(1+x+iy)^4]*[(7-x-iy)^3] [(1-2x-iy)^4]*[(3-x-iy)^3] (x+iy-1)^1/2

Homework Statement For which parameter \alpha\in\mathbb{R} the function: f(x, y)= \begin{cases}|x|^\alpha \sin(y),&\mbox{ if } x\ne 0;\\ 0, & \mbox{ if } x=0\end{cases} is differentiable at the point (0, 0)? The Attempt at a Solution For α<0, the function is not continue at (0, 0)...

Homework Statement If Z has a standard gaussian distribution then what is the distribution of Z2 and what is its mean? The Attempt at a Solution Let T = Z2 Then we can get that pdf T = e-T/2(1+1/T) x (1/√(2∏T) I am not sure if this is correct and don't know how to find the...

what did bell show concerning the existence of a local hidden variable model for quantum physics?

I learned in school that Median = L + (n/2-cf)*h/f where L = lower limit of median class n = no. of observations cf = cumulative frequency of class preceding the median class, f = frequency of median class, h = class size (assuming class size to be equal). I used to use this formula for...

Hello, Does anyone know if this makes sense or is usable? I've only been able to describe it through a graph. Instead of the x-axis being numbers, being powers of x. Let me clarify - where normally would be x=0,1,2,3... would now be x^0, x^1, x^2, x^3 and the y-axis would be values of...

Hi all I'm looking for solving this problem to find the closed form solution if it is possible: Y=\frac{1}{X} Where X is uniform random variable > 0 I know the expected value for X which is \overline{X} is there a method to find the expected value of Y which is \overline{Y} in term of...

Hey, I have a pdf of a random variable Z given. I am being asked to calculate what the moment generating function of a r.v Y= Z + c will be where c is a constant in ℝ I tried to calculate it in the following way: \int^∞_0 e^{(z+c)t} f(z+c)dz where f(z) is an exponential pdf with...

[FONT="Arial"]Hi Shaft A has variable RPM, getting input from some rotating element (say X), ranging from 0 to 2000. The RPM of X cannot be adjusted or controlled. A has to transfer the rotation with limiting RPM of upto 400 to Shaft B. Is there a way to limit the RPM using a mechanism...

Homework Statement Compute the limits of the following sequence (show your work): 3n+17n+3 4n5n-2 (sorry if it looks funny ... the top line is divided by the bottom line) The Attempt at a Solution I was thinking that I should get the exponents the same and add/subtract the...

Homework Statement This is a problem form my calculus book, which states: According to the ideal gas law, the pressure, temperature, and volume of a confined gas are related by P=kT/V, where K is a constant. Use differentials to approximate the percentage change in pressure if the temperature...

Homework Statement (x,y)-->(0,0) y*ln (y2+x2) Homework Equations ! The Attempt at a Solution i've tried polar coordinates i end up with sinθ in it don't know how to proceed and I've taken several paths like y=0 , x=0 , x=y2 , x=y , x=y3 they all yeild zero Edit : is it...

hi suppose we have this equation : d/dt(X)=A(t)*X x is a n by 1 column matrix and A is a n by n matrix that is the matrix of coefficients. coefficients of equations and consequently A are depend on t which is time. how i Solve this equation ? thanks

For X ~ N(μ, σ), what is P[|X-μ] < σ] in terms of the Q function? I know that P[|X-μ] < σ] can be decomposed into P[X > -σ + μ] + P[X < σ + μ] I'm not sure what to do next. i know P[X < σ + μ] can be expressed as 1 - phi(σ + μ - μ / σ) = Q(1), but I'm not sure how to approach P[X > -σ + μ]. I...

Let X and Y be independent and uniform on {1, 2, ... M} Find P(X > Y) so i know that P(X = x) = 1/M and P(Y = y) = 1/M i don't understand how Find P(X > Y) = (M+1)/2M

In an open domain in the plane (xU_{x}-yU_{y}-U)/U = (xV_{x} - y V_{y}+V)/V

Homework Statement Using the method of separation of variables, obtain a solution of the following PDE subject to the given conditions \frac{du}{dx}+y\frac{du}{dy}=(2x+y)u u(x,1)=5e^{x^{2}-x} Homework Equations The Attempt at a Solution See my attached working the...

Homework Statement The top-selling Red and Voss tire is rated 60000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 70000 miles and a standard deviation of 5000 miles. A: What is the probability that...

This is not homework. If you descend toward the ground in a helicopter, the density of the air is going to increase. I'm curious: Is the amount of energy required to turn the blades directly proportional to the density of the air? For instance: If the air density doubles, does the energy...

Hello everyone, My boss has asked me to find if there is any correlation between various sample parameters in a water quality study. We took around 150 samples, and for each one measured around 50 parameters e.g. iron content, free residual chlorine, level of coliforms, pH, etc etc. I...

Hi. I choose randomly a one word, and I decided to choose a word blue. Let random variable x be a length of the word blue. What is expected value and variance of a word blue? So, random variable x = 4. E(X) = [SIZE="5"]Ʃ xi fX(xi) i:xi∈S x1 + x2 + x3 + x4 = 10...

I had a second order differential equation where \psi is the unknown function and it is a function of x. We then introduced the following change of variable x = \sqrt{\frac{\hbar}{m \omega}} \xi. When all was said and done I found that, \frac{d^2 \psi}{d \xi^2} = \bigg(\frac{dx}{d...

Homework Statement Write a grammar that recognize a C variable declaration made up only of legal combinations of the following keywords: int char float double signed unsigned long short volatile const and a variable name. The grammar should be able to accepts all such legal declarations for...

The random variable X assumes the values 1,2,3 and 4 with equal probability. Find the density functions of the following variates: Attempted solutions: X 1 2 3 4 Pr(X) 1/4 1/4 1/4 1/4 a) Y=1-2X Y -1 -3 -5 -7 Pr(Y) 1/4 1/4 1/4 1/4 b) Z= X/(X+1) Z...

1. s = v0t + .5at^2 , solve for a 2. I don't know any 3. I don't know where to begin. I was thinking that you divide .5 from a to make it s/.5 = v0(t) + at^2.

I have a function in x and y, and I was trying to figure out if it was continuous or not. f(x,y)=\frac{x^2-y^2}{(x^2+y^2)^2} As far as I know, the only problematic point in the domain is (x,y)=(0,0) so I tried to use the \epsilon,\delta definition. My proposed limit at (0,0) being 0...

Let X be a discrete random variable that can assume the values -1, 0,1,2,3,4 with the probabilities 1/6, 1/12, 1/6, 1/4, 1/12, 1/4. Find the probability densities of the following random variables: a) Z= X^2 + 1 h(y)= f(g^-1(y)) Attempted Solution X= -1 0 1 2 3 4 Z=...

Ok, since nobody answered my last problem, I simplify. :) Let Z = γ1X1 + γ2X2, where the gammas are just constants p(Z) = exp(Z)/(1 + exp(Z)) X1 and X2 are bivariate normal and put Y = α + β1X1 + β2X2 + ε where ε ~ N(0,σ). Now, we want to find f(p(Z)|X1,Y). In this case, is it legal...

Good day All: How can I prove that a linear relationship exist between the displacement (d) and the capacitance(C) of a Variable dielectric capacitor? I know that the equation for a capacitor's capacitance is: C= εA/d

Homework Statement A block is acted on by a force that varies as (1.4*10^4N/m)x for 0<x<.21m , and then remains constant at 2940N for larger x. How much work does the force do on the block in moving it from x= 0 to x= 0.30m? How much work does the force do on the block in moving it from...

-16(2a) --> How to isolate variable? Homework Statement -16(2a) How do I isolate the variable? This is probably an EXTREMLY simple question. Its times like this that makes me wish I paid attention in high school algebra. The Attempt at a Solution Don't really know what to do...

Hi all, I have this kind of optimization problem: Variable to control: A=A=[a1;a2;...;am] objective function to minimize: L=A*TL where L is a scalar T is a matrix [1,m] TL is a matrix [m,1] constrain: Dt>Dtv where: Dt=[dt1;dt2;...;dtn] Dtv=[dtv1;dtv2;...;dtvn] is a...

Homework Statement When I'm solving problems, I'm told that the time between the vertical and horizontal components are the same. So that means that I would have to use the same time when calculating for both the vertical and horizontal components right? But then there are times when i have...

If the probability density of X is given by f(x) = {2(1 − x) for 0 ≤ x ≤ 1 {0 otherwise (a) Find the probability density function of Y1 = 2X − 1. I do not know how to start this problem can someone please help. Is there a formula that I am missing from my notes to solve this problem?

Under the assumption that the voltage is V_f\left(1-e^{-\frac{t}{RC}}\right), where V_f is the final voltage, how would I determine the relationship between current I and time t? I = \int_0^T \frac{V_f\left(1-e^{-\frac{t}{RC}}\right) - RI}{L} \,dt \, L the magnetic inductance, R the...

•• Working for a small gold mining company, you stumble across an abandoned mine shaft that, because of decaying wood shoring, looks too dangerous to explore in person. To measure its depth, you employ an audio oscillator of variable frequency. You determine that successive resonances are...

Can someone explain why 'dark matter' is the dominate explanation for the 'excess' gravity seen around galaxies? It seems to me that we have made an assumption that mass causes gravity. Isn't it possible that gravity arises from some as yet not understood mechanism? I may be way off base...

I am looking for a type of motor that can rotate gears and a large object and only rotate once every 12 hrs. I am having a hard time located one.

So I was sitting on the train last weekend, reading through my physics book on mechanical work and its relation to kinetic energy. One example would be that a box on a frictionless table being pushed and they would conclude that W = ΔK = ½mΔv2. Looking at this equation got me thinking...

Homework Statement Determine the value of k for which the system x + y + 2z = 3 x + 2y -4z = -3 2 + 8 + kz = -29 has no solutions. Homework Equations None The Attempt at a Solution Converting to a matrix 1 1 2 3 1 2 -4 -3 2 8 k -29 r2=r2-r1 1 1 2 3 0 1 -6 0 2 8 k -29...

Hey guys, I'm doing some multivariable calculus atm, and I need some help with the Domains of some multivariable functions... 1) f(x,y) = 3x^2 + 2y The problem I'm having here is I basically forget the definition of domain... would it be for all x and y even though there are two whole quadrants...