Let $X_n$ be a $\mathbb{N}$-valued random value. Suppose we have that \begin{equation} \frac{X_n-g(n)}{\sqrt{g(n)}}\sim N(0,1) \end{equation} for a function $g(n)$. This looks a lot like the Central Limit theorem - does this imply that $X_n\sim N(g(n),g(n))$ approximately? Or do we require that $X_n$ be replaced by the mean of $X_n$ for this? If so, what can we deduce about $X_n$ from this?
2026-04-04 03:49:20.1775274560
Central limit theorem application to general functions
51 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated 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 STATISTICS
- 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 $V$
- Fisher information of sufficient statistic
- Solving Equation with Euler's Number
- derive the expectation of exponential function $e^{-\left\Vert \mathbf{x} - V\mathbf{x}+\mathbf{a}\right\Vert^2}$ or its upper bound
- Determine the marginal distributions of $(T_1, T_2)$
- KL divergence between two multivariate Bernoulli distribution
- Given random variables $(T_1,T_2)$. Show that $T_1$ and $T_2$ are independent and exponentially distributed if..
- Probability of tossing marbles,covariance
Related Questions in STATISTICAL-INFERENCE
- co-variance matrix of discrete multivariate random variable
- Question on completeness of sufficient statistic.
- Probability of tossing marbles,covariance
- Estimate the square root of the success probability of a Binomial Distribution.
- A consistent estimator for theta is?
- Using averages to measure the dispersion of data
- Confidence when inferring p in a binomial distribution
- A problem on Maximum likelihood estimator of $\theta$
- Derive unbiased estimator for $\theta$ when $X_i\sim f(x\mid\theta)=\frac{2x}{\theta^2}\mathbb{1}_{(0,\theta)}(x)$
- Show that $\max(X_1,\ldots,X_n)$ is a sufficient statistic.
Related Questions in CENTRAL-LIMIT-THEOREM
- Another application of the Central Limit Theorem
- Prove that central limit theorem Is applicable to a new sequence
- On the rate of convergence of the central limit theorem
- Central limit theorem - Coin toss
- Example of central limit theorem fail due to dependence (for tuition)
- Example of easy calculations with the central limit theorem in higher dimensions
- Probability to have exactly 55 heads on 100 coin flips and CLT
- Chebyshev's inequality and CLT to approximate 1.000.000 coin tosses probability
- Lindeberg condition fails, but a CLT still applies
- Central limit theorem with different variance
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?