Maybe a stupid question but why is the case of independence of, say, two random variables $X$ and $Y$ is in some ways considered to be more ``central'' or more important than any other type of fixed dependence between $X$ and $Y$?
2025-01-12 19:14:15.1736709255
Why the case of independence of random variables is more important than any other specific type of dependence?
55 Views Asked by Alik https://math.techqa.club/user/alik/detail AtRelated Questions in PROBABILITY
- Given a random variable X, prove f(x) is a probability function.
- About conditional density function.
- Expected value & Lebesgue integral
- Feeling overwhelmed with this math explanation, what videos, courses, and books should I learn to help me digest this?
- In how many ways can 8 people be seated in a row? What is the probability that Al sits next to Bob?
- How to find probability after finding the CDF of a max?
- Does taking the limit of the inclusion-exclusion formula work here?
- What is the probability that the accumulated sum is L at some point?
- What is the probability of a power set of the sample space?
- Combinatorics Problem - Clients using two seperate services
Related Questions in PROBABILITY-THEORY
- Given a random variable X, prove f(x) is a probability function.
- What is the probability that the accumulated sum is L at some point?
- $f(t)-$a characteristic function. Prove that $|f(t)|$ does not have to be a characteristic function based on the example:
- Lower bound for the cumulative distribution function on the left of the mean
- What is the probability of the product rolled with 4 different dice being 24?
- Convergence in probability of random probability measures
- Proving that $N(\cdot \cap A)$ is a poisson random measure
- Why the case of independence of random variables is more important than any other specific type of dependence?
- Discrete probability - man getting caught cheating on public transport
- Show submartingale property.
Related Questions in RANDOM-VARIABLES
- $f(t)-$a characteristic function. Prove that $|f(t)|$ does not have to be a characteristic function based on the example:
- Find the density function of a random variable
- Why the case of independence of random variables is more important than any other specific type of dependence?
- limsup and liminf of sequence of random variables and Borel Cantelli
- For $r′ < r,$ show that $|X|^{r′} ≤ 1 + |X|^r $ and conclude that if $E|X|^r < \infty$, then $E|X|^{r′} < E|X|^r$ for all $0< r′ < r.$
- Calculate distribution of function of random variable using total probability formula
- Show that two random variables are independent.
- Indicator function, problem
- Variance of a non-linear function of a random variable
- liminf of sequence of iid random variables
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Refuting the Anti-Cantor Cranks
- Find $E[XY|Y+Z=1 ]$
- 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?
- What are the Implications of having VΩ as a model for a theory?
- How do we know that the number $1$ is not equal to the number $-1$?
- Defining a Galois Field based on primitive element versus polynomial?
- Is computer science a branch of mathematics?
- Can't find the relationship between two columns of numbers. Please Help
- 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
- A community project: prove (or disprove) that $\sum_{n\geq 1}\frac{\sin(2^n)}{n}$ is convergent
- Alternative way of expressing a quantied statement with "Some"
Popular # Hahtags
real-analysis
calculus
linear-algebra
probability
abstract-algebra
integration
sequences-and-series
combinatorics
general-topology
matrices
functional-analysis
complex-analysis
geometry
group-theory
algebra-precalculus
probability-theory
ordinary-differential-equations
limits
analysis
number-theory
measure-theory
elementary-number-theory
statistics
multivariable-calculus
functions
derivatives
discrete-mathematics
differential-geometry
inequality
trigonometry
Popular Questions
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- How to find mean and median from histogram
- Difference between "≈", "≃", and "≅"
- Easy way of memorizing values of sine, cosine, and tangent
- How to calculate the intersection of two planes?
- What does "∈" mean?
- If you roll a fair six sided die twice, what's the probability that you get the same number both times?
- Probability of getting exactly 2 heads in 3 coins tossed with order not important?
- Fourier transform for dummies
- Limit of $(1+ x/n)^n$ when $n$ tends to infinity