Variables Definition and 1000 Threads

In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol.
In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context.
A bound variable is a variable that was previously free, but has been bound to a specific value or set of values called domain of discourse or universe. For example, the variable x becomes a bound variable when we write:

For all x, (x + 1)2 = x2 + 2x + 1.
or

There exists x such that x2 = 2.
In either of these propositions, it does not matter logically whether x or some other letter is used. However, it could be confusing to use the same letter again elsewhere in some compound proposition. That is, free variables become bound, and then in a sense retire from being available as stand-in values for other values in the creation of formulae.
The term "dummy variable" is also sometimes used for a bound variable (more often in general mathematics than in computer science), but that use can create an ambiguity with the definition of dummy variables in regression analysis.

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  1. WMDhamnekar

    MHB How to use change of variables technique here?

    Find the volume V inside both the sphere $x^2 + y^2 + z^2 =1$ and cone $z = \sqrt{x^2 + y^2}$ My attempt: I graphed the cone inside the sphere as follows. But I don't understand how to use the change of variables technique here to find the required volume. My answer without using integrals is...
  2. M

    Probability that 𝑌>3𝑋 where 𝑋,𝑌 are 𝑁(0,1) random variables

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  3. WMDhamnekar

    Change of variables in multiple integrals

    Summary: Find the volume V of the solid inside both ## x^2 + y^2 + z^2 =4## and ## x^2 +y^2 =1## My attempt to answer this question: given ## x^2 + y^2 +z^2 =4; x^2 + y^2 =1 \therefore z^2 =3 \Rightarrow z=\sqrt{3}## ## \displaystyle\iiint\limits_R 1dV =...
  4. O

    MHB Partially Decoupled System with 3 variables

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  5. K

    I Alternative ways to quantize Ashtekar variables

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  6. LCSphysicist

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  7. Steve Zissou

    I Distribution of Sum of Two Weird Random Variables....

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  8. B

    A How to perform a fit with correlated variables

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  9. L

    Finding the distribution of random variables

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  10. K

    Using Poisson random variables to calculate this probability

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  11. F

    I Separation of Variables, but not equal to constant

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  12. S

    How do Computer Algebra Systems handle the scope of variables?

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  13. barryj

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  14. brotherbobby

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  15. brotherbobby

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  16. D

    Calculate the joint CDF of two random variables

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  17. chwala

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  18. D

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  19. chwala

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  20. M

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  21. S

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  22. anikad

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  23. cianfa72

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  24. SamRoss

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  25. cwill53

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  26. karush

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  27. karush

    MHB How to Solve Differential Equation with Separate Variables?

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  28. C

    Accessing class variables from .hpp file in the .cpp file

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  29. M

    Bound correlation coefficient for three random variables

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  30. chwala

    Determine the type of correlation for the two variables given in the data

    Kindly see the attached problem below (i find the topic to be easy and straightforward). My concern is only on the highlighted part: In my understanding, to define the type of correlation i have always approached a straightforward approach. For value ##1## perfect positive correlation and...
  31. B

    Mixed random variables problem

    I got (a) and (b) but I'm still working on (c). The solutions can be found here for your reference: https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041sc-probabilistic-systems-analysis-and-applied-probability-fall-2013/unit-ii/lecture-9/MIT6_041SCF13_assn05_sol.pdf. But...
  32. M

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  33. V

    Change of Variables: Integrals w/Polar Coordinates

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  34. PandaKitten

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  35. M

    Probability: Multivariate distribution change of variables

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  36. V

    Engineering equations involving correlated variables

    Hello, I'm carrying out an assignment on the simulation of correlated (random) variables. Can you suggest to me equations pertaining to the field of engineering (or science) that involve correlated variables? My question may sound redundant, because all equations create dependencies between...
  37. S

    Prob/Stats Material on complex random variables and exotic probabilities

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  38. JD_PM

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    All we should need for this problem are the basic rules for the Grassmann algebra \begin{equation*} \{ \theta_i, \theta_j\} = 0, \quad \theta^2_i=0 \end{equation*} \begin{equation*} \int d\theta_i = 0, \quad \int d\theta_i \ \theta_i = 1 \end{equation*} Starting from left to right...
  39. Leo Liu

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  40. M

    I Sum independent normal variables

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  41. anemone

    MHB Solving a System of 3 Equations with 7 Variables

    Let $x_1,\, x_2,\,\cdots,\,x_7$ be real numbers such that $x_1+4x_2+9x_3+16x_4+25x_5+36x_6+49x_7=1\\4x_1+9x_2+16x_3+25x_4+36x_5+49x_6+64x_7=12\\9x_1+16x_2+25x_3+36x_4+49x_5+64x_6+81x_7=123.$ Find the value of $16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7$.
  42. Y0SHI0N

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    Using the related equations, I have come up with an equation that I think would answer this question (#4). However, I was just wondering does the 'L' from equation #1 and 'l' in equation #3 cancels each other out when the substitution is made to give out equation #4 (since they are both the...
  43. redtree

    I Separation of variables for Named Probability Density Distributions

    Given a probability density distribution ##P(\vec{x})##, for what named distributions is the following true: \begin{equation} \begin{split} P(\vec{x}) &= P_1(x_1) P_2(x_2) ... P_n(x_n) \end{split} \end{equation}
  44. BWV

    I How do hidden variables supposedly explain radioactive decay?

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  45. I

    I Understanding the change of variables for PDEs

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  46. Armine

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  47. Celso

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  48. M

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  49. A

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  50. P

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