Let \(\{X_n\}\) be a sequence of random variables such that the following limits (in the regular point-wise sense) hold:\[\lim_{n \to \infty} \mathbb{E}[X_n] = c \quad \text{for some constant } c,\]and\[\lim_{n \to \infty} \text{Var}[X_n] = 0.\]Show that \(X_n\) converges to \(c\) in the mean-square sense, that is,\[\lim_{n \to \infty} \mathbb{E}[(X_n - c)^2] = 0.\]Hint: write \(\mathbb{E}[(X_n - c)^2]\) in a way that it involves \(\text{Var}[X_n]\).

Given that, Xn is a sequence of random variables. limn→∞EXn=c; for some constant c. limn→∞VarXn=0…

Let {Xn} be a sequence of random variables such that the following limits (in the regular point-wise sense) hold: and lim E[X₂] = c for some constant c, n→∞ lim Var[X₂] = 0. n→∞ Show that Xn converges to c in the mean-square sense, that is, lim E[(Xn-c)²] = 0. n→∞ Hint: write E[(X - c)²] in a way that it involves Var[Xn].

Let {Xn} be a sequence of random variables such that the following limits (in the regular point-wise sense) hold: and lim E[X₂] = c for some constant c, n→∞ lim Var[X₂] = 0. n→∞ Show that Xn converges to c in the mean-square sense, that is, lim E[(Xn-c)²] = 0. n→∞ Hint: write E[(X - c)²] in a way that it involves Var[Xn].

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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