Following is the equation: $$X = Y + Z.$$ $X, Y, Z$ are random variables. This is a random variable equation. What is the meaning of this equation? Does it mean that if you take any value of $Y$ and any value of $Z$, it should equal $X$? Or does it mean that when $Y$ and $Z$ are added, then $Y+Z$ will have same distribution as $X$?
2026-04-01 23:31:31.1775086291
What is the mathematical interpretation of random variable equation?
118 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in PROBABILITY
- How to prove $\lim_{n \rightarrow\infty} e^{-n}\sum_{k=0}^{n}\frac{n^k}{k!} = \frac{1}{2}$?
- Is this a commonly known paradox?
- What's $P(A_1\cap A_2\cap A_3\cap A_4) $?
- Prove or disprove the following inequality
- Another application of the Central Limit Theorem
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- A random point $(a,b)$ is uniformly distributed in a unit square $K=[(u,v):0<u<1,0<v<1]$
- proving Kochen-Stone lemma...
- Solution Check. (Probability)
- Interpreting stationary distribution $P_{\infty}(X,V)$ of a random process
Related Questions in PROBABILITY-THEORY
- Is this a commonly known paradox?
- What's $P(A_1\cap A_2\cap A_3\cap A_4) $?
- Another application of the Central Limit Theorem
- proving Kochen-Stone lemma...
- Is there a contradiction in coin toss of expected / actual results?
- Sample each point with flipping coin, what is the average?
- Random variables coincide
- Reference request for a lemma on the expected value of Hermitian polynomials of Gaussian random variables.
- Determine the marginal distributions of $(T_1, T_2)$
- Convergence in distribution of a discretized random variable and generated sigma-algebras
Related Questions in PROBABILITY-DISTRIBUTIONS
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- Statistics based on empirical distribution
- Given $U,V \sim R(0,1)$. Determine covariance between $X = UV$ and $V$
- Comparing Exponentials of different rates
- Linear transform of jointly distributed exponential random variables, how to identify domain?
- Closed form of integration
- Given $X$ Poisson, and $f_{Y}(y\mid X = x)$, find $\mathbb{E}[X\mid Y]$
- weak limit similiar to central limit theorem
- Probability question: two doors, select the correct door to win money, find expected earning
- Calculating $\text{Pr}(X_1<X_2)$
Related Questions in RANDOM-VARIABLES
- Prove that central limit theorem Is applicable to a new sequence
- Random variables in integrals, how to analyze?
- Convergence in distribution of a discretized random variable and generated sigma-algebras
- Determine the repartition of $Y$
- What is the name of concepts that are used to compare two values?
- Convergence of sequences of RV
- $\lim_{n \rightarrow \infty} P(S_n \leq \frac{3n}{2}+\sqrt3n)$
- PDF of the sum of two random variables integrates to >1
- Another definition for the support of a random variable
- Uniform distribution on the [0,2]
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Random variables are defined as measurable functions from a probability space $\Omega$ into some target space. Without any further context, I interpret that equality as an equality of functions, e.g. $X(\omega) = Y(\omega) + Z(\omega)$ for every $\omega \in \Omega$. Quite often in probability, we only care about equality on a set of measure 1, and it is common to see $X = Y+Z$ a.s. where a.s. is an abbreviation for almost surely, which means that the functions $X$ and $Y+Z$ might differ on a tiny set of measure 0, but we don't care.