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3. Suppose X₁,..., Xn are iid with mean and variance o2 <∞o. Let Xn be the san (a) State the definition of convergence in distribution of a sequence of random variables. (b) Find the limiting distribution of Xn- (c) What is the limiting distribution of the random variable √n(Xn-u)/o? State the central limit theorem.

3. Suppose X₁,..., Xn are iid with mean and variance o2 <∞o. Let Xn be the san (a) State the definition of convergence in distribution of a sequence of random variables. (b) Find the limiting distribution of Xn- (c) What is the limiting distribution of the random variable √n(Xn-u)/o? State the central limit theorem.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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3. Suppose \( X_1, \ldots, X_n \) are iid with mean \( \mu \) and variance \( \sigma^2 < \infty \). Let \( \bar{X}_n \) be the sample mean. (a) State the definition of convergence in distribution of a sequence of random variables. (b) Find the limiting distribution of \( \bar{X}_n \). (c) What is the limiting distribution of the random variable \( \sqrt{n}(\bar{X}_n - \mu)/\sigma \)? State the central limit theorem.
Transcribed Image Text:3. Suppose \( X_1, \ldots, X_n \) are iid with mean \( \mu \) and variance \( \sigma^2 < \infty \). Let \( \bar{X}_n \) be the sample mean. (a) State the definition of convergence in distribution of a sequence of random variables. (b) Find the limiting distribution of \( \bar{X}_n \). (c) What is the limiting distribution of the random variable \( \sqrt{n}(\bar{X}_n - \mu)/\sigma \)? State the central limit theorem.
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