Variable Definition and 1000 Threads

If X is a continuous random variable and g is a continuous function defined on X (Ω), then Y = g(X ) is a continuous random variable. Prove or disprove it.

If X is a random variable distributed uniformly in [0, Y], where Y is geometric with mean alpha. i) Is this definition valid for uniform distribution ? ii) If it is valid, what is the pdf of the transformation Y-X?

15+1/2=0.60(20x)

Create the Euler-Lagrange equation for the following questions (if it's necessary change the variables). Homework Statement $$\tag{1}\int _{y_{1}}^{y2}\dfrac {x^{'}{2}} {\sqrt {x^{'}{2}+x^{2}}}dy$$ $$\tag{2}\int _{x_{1}}^{x_{2}}y^{3/2}ds $$ $$\tag{3} \int \dfrac {y.y'} {1+yy{'}}dx...

If one has a simple variable coefficient process like y'(t) = r(t)*y(t), is there a way to control it to a set point by feedback hitting the variable coefficients in r(t)? I am interested in feedback control of population processes. y'(t) = r*y(t) is simple proportional growth with a...

I remember learning at one point that you can put some sort of symbol on top or near a variable to indicate that it is being held constant. I thought that it was just a bar drawn above the variable but in some cases, it means "the average of." Anyone know what I'm talking about?

Homework Statement f(x,y) = (x-y) / (x+y) Calculate Δf and df for the change of point (3,2) to point (3.2, 2.1) Homework Equations The Attempt at a Solution I guess that I have to use limits, but don't know how to begin with.

How do you make a differential equation for such? Say for example. I have two reactions in series, A → R and R → S going in a gas-phase reaction. If I'm correct, the ODE for the conversion of A is dXA/dt = kA*[(NAo/vo)*(1-XA)/(1+δA*YAo*XA)]*[(vo/NAo)*(1+δA*YAo*XA)]. I don't know now...

I'm having a bit of a problem proving the second condition for a martingale, the discrete time branching process Z(n)=X(n)/m^n, where m is the mean number of offspring per individual and X(n) is the size of the nth generation. I have E[z(n)]=E[x(n)]/m^n=m^n/m^n (from definition E[X^n]=m^n) =...

What is the variable "theta of omega" in a series RL cct? Homework Statement Hi I'm not looking for a complete solution to this problem. My question concerns just one specific part of the solution to part A: why is tan θ(ω) = ωL/R? and what θ(ω) represent? how does it relate to the...

Homework Statement Calculate the capacitance of a spherical capacitor of inner radius A and outer radius B which is filled with a di-electric varying as e=c+dcos^2θ . c and d are constants and θ is the angle made with the z axis.(also known as the polar angle) Homework Equations $C=εA/d$The...

Hi, Homework Statement How may I find to what number Ʃ(m=1 to ∞) m/2m-1 converges? Further, suppose I know it converges to 4, why would then E(Y), given that P(Y) = 1/2m-1, be equal to 2 (thus asserted the answer) and not 4? Homework Equations The Attempt at a Solution I am...

Hi to everybody Homework Statement I´ll show the problem with a picture: Homework Equations L\overline{x}=∫xc ρ dl The Attempt at a Solution Well the total length of the rod is 1 feet, I only need to calculate the integral. The moment xc of a differential element of mass of the rod is...

If I have a variable X whose gaussian distribution is known and let f be a known function, is there a way to compute f(X) (i.e) the resulting gaussian distribution from this? Is the result actually a gaussian distribution?

Homework Statement A particle which moves with a constant acceleration in a straight line passes through the point O, A and B in that order. If the distances OA and AB are 17 m and 35 m respectively and the particle takes the same amount of time , 3 seconds to travel each distance then...

hi.. with refrenence to http://www.math.uah.edu/howell/MAPH/Archives/Old_Notes/PDEs/PDE1.pdf page 7, “Observe” that the only way we can have formula of t only= formula of x only is for both sides to be equal to a single constant. here I do understand that for these to being equal...

i need to solve for a variable inside the error function on excel, is there an opposite function i can use to accomplish this? example: y = sqrt(x-t) -> x = t+y^2 except instead of a sqrt( ) I have erf( ) **this is not a math class so I don't have to get into breaking it down into the...

Problem: Suppose that $X \text{ ~ Exp}(\lambda)$ and denote its distribution function by $F$. What is the distribution of $Y=F(X)$? My attempt: First off, I'm assuming this is asking for the CDF of $Y$. Sometimes it's not clear what terminology refers to the PDF or the CDF for me. $P[Y \le y]=...

This is something that when I see the work done it makes sense, but I find it difficult to do myself. I'm also aware there is an explicit formula for doing this but that involves Jacobians and a well-defined inverse, so I think it's more intuitive to do it step-by-step. Problem: Suppose $X...

Professor Roberto has to take an oral examination. The grading scale is as follows: 5: = best and 1: = worst. At most he only gives the note 4. Each student under review is questioned if he is a Lakers fan. The student's grade is based on his answer (is a fan / not a fan) and on the language in...

Homework Statement X is uniformly distributed over [-1,1]. Compute the density function f(y) of Y = 2X2 + 1. Homework Equations The Attempt at a Solution FY(Y) = P(Y < y) = P(2X2 + 1 < y) = P(X < +\sqrt{1/2(y-1)} = FX(+\sqrt{1/2(y-1)}) We have that f(x) = 0.5 for -1 < x <...

Hi guys, first time poster. My question is; How would a constant damping provided by an electromagnet affect the damping ratio (and logarithmic decrement) amplitude? And how would increasing the current through the electromagnet affect the damping? So far I've found Biot-Savart's Law which...

Homework Statement Use * to show --> Homework Equations The Attempt at a Solution So I've begun by trying to take the 2nd derivative of \frac{\partial z}{\partial r}=\cos\theta\frac{\partial z}{\partial x}+\sin\theta\frac{\partial z}{\partial y} Which gives me this...

Homework Statement An electric circuit comprises two series resistors A and B, the first of which has a given resistance R_A and the second variable resistance R_B, over which a constant DC voltage U is added. How shall the resistance R_B be selected so that the power P developed in resistor B...

Just wondering if the Java experts here could help me. As part of a project I'm making a function rand9() that returns a pseudo-random number 0 through 9. The problem is that each time it's called I need a certain number to increment so that it can generate a new (not necessarily different)...

Hi All, I built this shaker table: and I am now trying to change the amplitude so that it is no longer fixed but instead variable. The frequency I can change but the amplitude is fixed given this design. Does anyone have any suggestions on how to be able to change the amplitude so I can...

Homework Statement A balloon of mass M contains a bag of sand of initial mass ##m_o##. The balloon experiences a constant upthrust and is initially at rest and in equilibrium: the upthrust compensates exactly for the gravitational force. At time t=0, the sand is released at a constant rate...

Homework Statement There is a uniform but variable magnetic field ##\vec{B}=(B_0 t)(-\hat{k})##, in a cylindrical region, whose boundary is described by ##x^2+y^2=a^2##. ##\displaystyle \int_P^{Q} \vec{E} \cdot \vec{dy}## is (see attachment 1) A)0 B)##\frac{\pi}{4}(B_0 a^2)##...

This is my first time posting in this forum, I am not very familiar with the rules. I am a year 1 physics student, and I had only taken 1 variable calculus( I also know some basic linear algebra, e.g. how to calculate eigenvector in 2x2 situation, don't know Gram–Schmidt process for...

Homework Statement Give a method for generating a random variable with distribution function F(x) = 1/2(x+x^{2}) 0<x<1 The Attempt at a Solution From what i can tell i am supposed to do something like: Let U be a uniformly distributed random variable over (0,1). U =...

The cumulative distribution function of a continuous random variable is given as follows: 0 0 ( ) 0 5 5 1 5 X if x x F x if x x           a. Determine and name the density function of . [02] b. Use both and ( ) X F x to find P(X  3) . [05] c. Find the variance of ...

Homework Statement (Everything here is frequency dependant, but I have left off the v from all the variables to minimise chance of typos - hopefully that is ok but please let me know if not and I will try and retype!) The equation of radiative transfer is dI/dτ = -I + S We guess...

Is there an easy way of designing a band pass filter whose pass band could be varied over a certain band?? The pass band is in MHz range. Thanks

f(x)=1, θ-1/2 ≤ x ≤ θ+1/2 Given that Z=(b-a)(x-θ)+(1/2)(a+b) how would you show that Z has a continuous uniform distribution over the interval (a,b)? Any help would be much appreciated.

Calculate max and min value of the function f(x,y)=x^2+y^2-2x-4y+8 in the range defined by the x^2+y^2≤9 Progress: f_x(x,y)=2x-2 f_y(x.y)=2y-4 So I get x=1 and y=2 We got one end point that I don't know what to do with x^2+y^2≤9 If I got this right it should be a elips that x can max be 3,-3 and...

Homework Statement X is a normal random variable with mean 1, variance 4. 1. Find P( X(X-1) > 2 ) 2. Find a value 'a' for which P(|X| > a ) = .25 The Attempt at a Solution I had no idea how to start 1. For 2, i got this far then got stuck: P(|X| > a) = 1 - P((X-1)/2 <=...

Homework Statement Determine if sequence converges or diverges, if it converges find its limit. a (sub) n= (3^(n+2))/(5^(n)) The Attempt at a Solution The only things I've tried doing thus far is setting the sequence up as a function and letting x approach infinity. I then tried using l...

so i have swap.s .text main: la $a0,n1 la $a1,n2 jal swap li $v0,1 # print n1 and n2; should be 27 and 14 lw $a0,n1 syscall li $v0,11 li $a0,' ' syscall li $v0,1 lw $a0,n2 syscall li $v0,11 li $a0,'\n' syscall li $v0,10 # exit syscall swap: L1: .data n1: .word 14 n2...

Homework Statement lim(x,y)-(1,0) ln((1+y^2)/(x^2+xy)) Homework Equations The Attempt at a Solution if i just substitude x and y i get ln (1)= 0 so is the limit 0?

I have the following integral: \int_0^{f(x,y)}{f' \sin(y-f')df'} Now suppose that f(x,y) = x*y, my question is how do I write the integral in terms of x and y only? Can I do something like this? Since df=\frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy we can obtain...

First of, I apologize for the vague title, I didn't know how to summarize this issue. Homework Statement Suppose that the interest rate obtained in month i is a random variable Ri with the uniform distribution on [0.01, 0.03], where R1,R2, . . . are independent. A capital of 1 unit...

Homework Statement ((1/3)(y^3))+(1/y)=.5*ln((x^2)+1) Solve in terms of y Homework Equations The Attempt at a Solution I am in college differential equations, and i just can't solve in terms of y. y teacher wants that...i tried wolfram alpha, etc. How on Earth do you factor this...

Hi, I'm trying to solve this equation inside of Maple: http://screencast.com/t/EeqzLhxS for gamma(s) I assign variables to each of the values like this:http://screencast.com/t/DBLS8BH6R When I try to solve I get this weird answer with a new _z variable...

I have the following recurrence equation, where C is just some constant: $$ T(n) = 0, n = 1\\ T(n) = T(\frac{n-1}{2}) + 2C, n > 1 $$ Using a top-down approach to unrolling the equation to find the pattern, I get: $$ T(n) = T(\frac{n-k}{2^{k}}) + 2kC $$ Now I want to solve for k and associate...

Hi, I am working on an economics paper, and I find that the following first order condition for my variable of interest (\mu \in [0,1]): \frac{\lambda(1+\mu)}{(1-\mu)}=N-x\frac{(1+\mu)}{\sqrt{\mu}} I would ideally like to provide an explicit solution, but unfortunately, this would amount to...

I have a problem that I normally find solutions to via trial and error, and they usually aren't optimized, but was wondering if there is a better way to solve this and optimize. My application is specific but this is the best way I can describe the problem. Forgive me if it doesn't make...

Homework Statement I'm trying to find the value of a variable which happens to be an exponent. Homework Equations 230,000=1500\frac{(1+.00077)^n-1}{.00077} I believe I need to use logarithms to get to my answer, but I've reviewed logarithm rules and I'm stuck. The Attempt at a...

Dear all, I am stuck with an apparently easy system of 3 simultaneous equations that has to be solved in x,y and z. The system is the following: ##(y+z) / ((x+y+z)²)=ax^{α-1}## ##(x+z) / ((x+y+z)²)=by^{α-1}## ##(x+y) / ((x+y+z)²)=cz^{α-1}## The parameters (a,b,c) and the variables (x,y,z) are...

many transition elements have variable oxidation state like Fe.what is the exact cause for this?they may not obey the octet rule,but what is the reason behind this?Also,elements like nitrogen are not transition elements and still show variable valency.what will be the electronic configuration of...

Homework Statement A trial consists of throwing two dice. The result is counted as successful if the sum of the outcomes is 12. What is the probability that the number of successes in 36 such trials is greater than one? What is this probability if we approximate its value using the Poisson...