What is Variable: Definition and 1000 Discussions

A variable star is a star whose brightness as seen from Earth (its apparent magnitude) fluctuates.
This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either:

Intrinsic variables, whose luminosity actually changes; for example, because the star periodically swells and shrinks.
Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth; for example, because the star has an orbiting companion that sometimes eclipses it.Many, possibly most, stars have at least some variation in luminosity: the energy output of our Sun, for example, varies by about 0.1% over an 11-year solar cycle.

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  1. M

    Exponential Random Variable

    Hi, I have a quick question. Let R and S be two independent exponentially distributed random variables with rates λ and μ. How would I compute P{S < t < S + R}? I am a little bit confused because of the variables on either side of the inequalities. I have tried conditioning on both S and R...
  2. D

    MHB How can I use variable transformation to obtain a solution for this ODE?

    Given the following ODE \[ \left(\frac{du}{dx}\right)^2 = \mu u^2 - \frac{2\alpha}{\sigma + 2}u^{\sigma + 2} - \frac{\gamma}{\sigma + 1}u^{2(\sigma + 1)} \] How do I obtain \[ u(x) = \left(\frac{A}{B + \cosh(Dx)}\right)^{1/\sigma} \] where \(A = \frac{(2 + \sigma)B\mu}{\alpha}\), \(B =...
  3. R

    Strange Change of Variable of Integration

    I've been following a few derivations for quantities in classical mechanics of rotating systems, and one of the integrals is transformed in a way I've never seen before. For angle theta, angular velocity omega and angular acceleration alpha: Intuitively I can see that they've 'just' swapped...
  4. C

    Java Java error with variable initialization

    import java.util.Scanner; import java.io.FileNotFoundException; import java.io.FileReader; import java.io.IOException; import java.io.PrintWriter; public class CountryPopulationReverse{ public static void main(String args[])throws FileNotFoundException { //Variable...
  5. F

    MHB Dividing vs Subtracting to Solve Equations w/1 Variable

    If you have the equation \frac{dx}{dt}=4(x^2+1) I sometimes get confused if i should should subtract 4(x^2+1) from both sides or multiply by it's reciprocal. If I subtract from both sides then I'd have 0 on the right side and that would give a different answer after integration but...
  6. L

    Difference between a variable and a constant?

    I know this is a very elementary question, but I suddenly realized in calculus that I don't really know precisely what the definition of a variable and constant was. I know what people tend to call constants and variables in something like: ax + by = c, where you'd call x and y a variable...
  7. S

    Random Variable and Distribution Function Relationship

    I'm in a probability theory class and I feel like I'm missing something fundamental between random variables and their distribution functions. I was given the following questions: 1)Let θ be uniformly dist. on [0,1]. For each dist. function F, define G(y) = sup{x:F(x)≤y}. Prove G(θ) has the...
  8. M

    What are the equations for conic sections in 4 dimensions?

    Homework Statement The problem is given in the picture attached. However we are given the equation of a 4 dimensional shape with certain choice given to explain the shape in that dimension. Homework Equations Equations of different shape such as: sphere: √(x^2+y^2+z^2) = r...
  9. A

    Variable acceleration and terminal velocity

    Homework Statement A cube is falling from a height of 200 m (initial velocity =0) , it reaches it's terminal velocity . Given that :its mass is 100 kg , cross sectional area 40 cm2 and coefficient of drag 2. Putting only weight and drag in consideration , calculate its terminal velocity and...
  10. W

    MHB Need Explanations For The Red Part (2 variable inequality)

    Prove that for any two numbers x,y we have [(x^2 + y^2)/2] >= x + y - 1 Solution) For any number a we have have a^2 > 0. So, (x-1)^2 + (y-1)^2 >= 0 And if we solve this we get the solution.I don't get the red part.
  11. R

    (Probability/Statistics) Transformation of Bivariate Random Variable

    Homework Statement Let X_1, X_2 have the joint pdf h(x_1, x_2) = 8x_1x_2, 0<x_1<x_2<1 , zero elsewhere. Find the joint pdf of Y_1=X_1/X_2 and Y_2=X_2. Homework Equations p_Y(y_1,y_2)=p_X[w_1(y_1,y_2),w_2(y_1,y_2)] where w_i is the inverse of y_1=u_1(x_1,x_2) The Attempt at a Solution We can...
  12. M

    Partial derivative that contains the independent variable as an deriva

    Homework Statement \frac{\partial f}{\partial t},\frac{\partial f}{\partial x} where f=f(x,t,\frac{dx}{dt}) Homework Equations The Attempt at a Solution I think it's impossible to consider it as a simple partial derivative.
  13. N

    MHB Conditional PDF of this random variable

    the random variable X and Y have a joint PDF given by: $f_{x,y}(x,y) = \frac{1}{10}$, $(x,y)\in[-1,1] * [-2,2] \cup [1,2] * [-1,1]$ a) find the conditional PDF for $f_{y|x}(x,y)$ and $f_{x|y}(xy)$ and b) find E[X|Y], E[X] and Var[X|Y]. Use these to calculate var(X) for part a) I am unsure...
  14. A

    An inequality for a two variable function

    Suppose that ##F(u,v)=a|u+v|^{r+1}+2b|uv|^{\frac{r+1}{2}}##, where ##a>1, b>0## and ##r\geq3.## How we can show that there exists a positive constant c such that ## F(u,v)\geq c\Big( |u|^{r+1}+|v|^{r+1}\Big). ##
  15. S

    MHB Dealing with 5 input variable Kmaps

    Just need someone to check my work. Thank you for your time. First time doing a 5 input Kmap. Determine the following 5 input Karnaugh map for function f(V,W,Z,Y,Z) determine the minimal SOP equation. NOTE: (WX are the variables associated with the top column, and YZ are the variables...
  16. P

    Generating level surface from 2 variable function

    Homework Statement given f(x,y)=9/(x+y) find a level surface. Homework Equations The Attempt at a Solution g(x,y,z)=f(x,y)-z=0? g(x,y,z)=9/(x+y) -z=0? That answer is wrong. Apparently i must have the following: g(x,y,z)=z(x+y)=9 How do I solve problems like these? Another...
  17. PsychonautQQ

    Variable Resistors in a Voltage Divider

    My textbook says that in a voltage divider (voltage source Vin, then a resistor, then another path that leads to Vout, Resistor two, Ground, that it is a bad idea to use variable resistors for BOTH of the resistors (but it is okay if you just do one or the other). Does anybody know why?
  18. G

    Why does the multi variable chain rule need to be proven?

    It seems to me to follow from the definition of a partial derivative. If f(x,y) = fx + fy, then what else can Δf be other than ∂f/∂x*Δx + ∂f/∂y*Δy? Then in the limiting case, the changes in f, x and y becomes differentials instead. All this seems to be given by the definitions themselves, is...
  19. BruceW

    Extrinsic thermodynamic variable confusion

    Hi all, Something has been troubling me. To begin with, I have never been certain about this concept of 'extrinsic' thermodynamic variables. I mean, they don't have to be linear with system size, right? They just need to increase with system size? And also, I have a specific 'example problem'...
  20. M

    Find E[(X-mu)^k] - Normal Random Variable

    Hi, I'm having a bit of a problem with a probability question. The question is Let X be a normal random variable with mean \mu and variance \sigma^{2}. Find E[(X -\mu)^{k}] for all k = 1,2,... I'm not really sure what to do and need some help to confirm how to approach the question...
  21. D

    Valid Variable Names: Rules & Tests

    Hi all, I would like to clarify regarding valid variable names. Well what I fairly understand are the rules regarding names.. What I am unsure about is -- in a test, is there any way to spot a reserved name? For example to make things difficult, trick question, sometimes the question will...
  22. F

    MHB Determining if equation is linear in indicated dependent variable

    I was stuck on a question and went back to look at an example but couldn't understand the example. It has (y-x)dx +4xy dy = 0 is linear in y because it can be written as 4xy'+y=x First of all what are dx and dy doing in the equation? They look to be from the end of an integral. Second, how did...
  23. X

    String with variable density

    Homework Statement The linear mass density in a string is given by μ = μ0[1 + cos(x/R)] where R is a constant. If one averages this density over the large size L it becomes uniform: <μ> = μ0, where <…> means averaging. What is the minimum size L (in terms of R) such that the density can be...
  24. J

    Variable MOI: Rotational 2nd Law

    I'm having trouble finding any sources that discuss equations of motion that take into account a changing moment of inertia. Just looking at the scaler case, angular momentum is L = I\omega Then, according to the 2nd law, \tau = \frac{d}{dt}(L) = \dot{I}\omega + I\alpha Is this correct...
  25. B

    Research topics in Variable stars

    Hey, I am an undergraduate physics & astronomy student. I am looking for a good research topic to work on for this semester. I have access to a .5 m telescope in Louisville, Ky (38 deg N), a .5 m telescope, and possibly another with a built in spectroscopy as well as photometry capabilities...
  26. naima

    Can hidden variable theories assign values to observables?

    hi PF I read the no-go Kochen theorem using 18 vectors projection (here). One attribute a value to an observable A: v(A) This function is supposed to be linear and verify v(AB) = v(A) v(B) so v(AB - BA) = v(A)v(B) - v(B)v(A) = 0 (v is a real number function) v must assign v(id) = 1 because v(A...
  27. T

    Variable Frequency Drive vs. Servo Drive

    I'm wondering what the difference is between a VFD and servo drive are. I'm pretty familiar with VFDs but not so much with servo drives. From what I read, would the following assumptions be correct? A variable frequency drive without an encoder module will adjust the frequency and amplitude...
  28. J

    Define the function of density of the random variable Y.

    We selected X point from interval (-1,2). If X=x, we selected point Y from (-1,x^2). Define the function of density of the random variable Y.
  29. Saitama

    Variable mass system - sand falling on flatcar

    Homework Statement A flatcar of mass ##m_0## starts moving to the right due to a constant horizontal force F. Sand spills on the flatcar from a stationary hopper. The velocity of loading is constant and equal to ##\mu## kg/s. Find the time dependence of the velocity and acceleration of flatcar...
  30. C

    Change of variable for 2nd partial differentiation and higher.

    Hello, the question I have arises from the 4th Edition of the book "Advanced Engineering Mathematics" written by K.A. Stroud. For those who owns the book, it is the example #2 starting at page 379. More precisely, the example is separated into two parts but the first one is very straight...
  31. P

    Can we rewrite Schrodinger equation using observable variable?

    We know that in Schrodinger equation, Ψ is called wave function, which is not observable, while Ψ·Ψ* is the probability, which is observable. can we rewirte the Schrodinger equation to a form without Ψ but only Ψ·Ψ*? because I think, in this way can I figure out all conservations in the...
  32. S

    MHB Derivative with respect to which variable?

    We have the following trapezoid: The question is to find the length of the fourth side when the area of trapezoid is maximized. I realize we will not be able to find a numerical value for the fourth side due to the given information (rather, lack thereof). So we are essentially going have...
  33. M

    Inverse function of a two variable function

    Homework Statement I'm wondering how to find the inverse function of some f(x,y)? Homework Equations The Attempt at a Solution
  34. M

    Maximize two variable equation

    Hello, This will probably sound like a HW question, but it's not. There is a certain phone system that I can use to call someone. There is an outgoing charge per call and a per minute charge. The per minute charge is $ 7/18 The outgoing call charge is $299/90 Say I have $50 on the...
  35. L

    Prove convergence in probability for n * Poisson variable to zero

    The problem: Let \mu_{n} = \frac{1}{n} for n \in \mathbb{N}. Let X_{n} \; \mathtt{\sim} \; \textrm{ Poisson}\left( \lambda_{n} \right). Let Y_{n} = n X_{n}. Show that Y_{n} \xrightarrow{P} 0 . Work I've done: I've shown that X_{n} \xrightarrow{P} 0 by showing that \mathbb{P} \left(...
  36. G

    Differential Equation with Function of Shifted Variable

    Hey guys, I have a question for you... how would one go about solving an equation like this... or this... This came across my mind the other day. I was wondering how to solve that equation if the function is of t-1, instead of t. Obviously, if it was f(t), the solution would be Ce^t, but I was...
  37. M

    Variable of an equation is in the denominator

    Homework Statement 1/x - 1/a = 1/b Solve for x Homework Equations The Attempt at a Solution I used to be able to do this in high school, but now I am 43! Normally, I would just cross-multiply and solve for x, to get the x out of the denominator, but you cannot...
  38. O

    How to integral ? How can they ignore that variable?

    Homework Statement I don't understand case 1. In case 2 that is normal integration , isn't? Then why case 1 can simply ignore the r ? I don't think r is constant. Homework Equations The Attempt at a Solution Please guide. Thanks
  39. E

    What's the expected value of this problem (random variable)?

    Homework Statement What's the expected value of this problem (random variable)? X: represent the result of dice number 1 - result of dice number 2 example dice 1 first roll = 2; second roll = 3 dice 2 first roll = 1; second roll = 2 X = 2+3 -(1+2) = 2 what's the expected value...
  40. Jeffack

    Generate a Multivariate Random Variable

    Hi, I'm an economics graduate student doing some work on a nested logit model. I am trying to generate random variables that follow the following CDF: F(x_1, x_2) =\textrm{exp}[ -(e^{-2x_1}+e^{-2x_2}) ^{1/2}] (This is an extreme-value distribution) With a single random variable, I...
  41. I

    Jacobian Determinant/ mult. variable implicit differentiation

    Homework Statement Let F: x^2 + y^2 - z^2 + 2xy - 1 = 0 and G: x^3 + y^3 - 5y - 4 = 0. Calculate dz/dx. Note: This is NOT the partial derivative ∂z/∂x. I do not need help in taking the derivative of many polynomials. What I need help in is setting up a Jacobian determinant to evaluate this...
  42. P

    Who first studied variable speed of light? - Einstein

    Who first studied variable speed of light? --- Einstein Variable speed of light is a hypothesis that states that the speed of light, usually denoted by c, may be a function of space and time. Einstein's first mentioned a variable speed of light in 1907, and he reconsidered the idea more...
  43. C

    Covariance Matrix of a Vector Random Variable w/ Components Related

    Homework Statement Given X=ZU+Y where (i) U,X,Y, and Z are random variables (ii) U~N(0,1) (iii) U is independent of Z and Y (iv) f(z) = \frac{3}{4} z2 if 1 \leq z \leq 2 , f(z)=0 otherwise (v) fY|Z=z(y) = ze-zy (i.e. Y depends conditionally on...
  44. trash

    [Probability] Expected Value of Random Variable

    Homework Statement A man wants to travel to four cities (A,B,C,D) but he has such a bad memory that he can't remember the cities that visited, therefore, if he travel to city A he can choose between (B,C,D) and if he then travel to B he can choose between (A,C,D). Find v, If v it's the...
  45. H

    MHB PGF of a conditional random variable

    I have a queueing system. The probability Generating Function of the number of packets in the queue (queue length) is given by Q_G(z)=\frac{e^{\lambda T(z-1)}(1-z^{-1})(1-\lambda T)}{1-z^{-1}e^{\lambda T(z-1)}}. I need to find the PGF of a conditional quantity. X=(Q_G|Q_G>0) i.e. to say in...
  46. K

    Question on variable definitions in Paschens law? (breakdown voltage)

    Hello all, In the equation V= apd/Ln(pd)+b as described by Paschens law regarding breakdown voltage, I was wondering what the "L" and the "n" stood for. Example of what I'm looking for: p stands for pressure. Thanks.
  47. A

    Magnitude of the tension when there is static (variable) friction

    Hello folks, I'm being tricked by the pesky friction force again. I know that static friction acts just to put everything in equilibrium as long as its magnitude doesn't exceed a certain value. That is ok. But when there are other adjustable force such as TENSION and NORMAL, (which in this...
  48. A

    I do not understand Variable density

    Hey forum I need to ask for a link to a page for Variable density or preferably an explanation from someone who can describe it simply. I am trying to teach myself about the function of Qubits and have run into probability density functions and cannot find a good reference on what exactly...
  49. B

    MHB Proving of Y=g(X) as a continuous random variable

    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.
  50. H

    MHB Transformation of Random Variable

    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?
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