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Let (Xn} be a sequence of rv's such that X, is distributed as Z with probability pn and as onZ with probability 1- Pn where Z~ N(0, 1), pn →pe [0,1] and on→ o. |(a) Show that X, X if and only if p =1. What is the distribution of X? |(b) lim, Var(X„) is not necessarily the same as Var[X]. Find the possible values of lim, Var[X,).

Let (Xn} be a sequence of rv's such that X, is distributed as Z with probability pn and as onZ with probability 1- Pn where Z~ N(0, 1), pn →pe [0,1] and on→ o. |(a) Show that X, X if and only if p =1. What is the distribution of X? |(b) lim, Var(X„) is not necessarily the same as Var[X]. Find the possible values of lim, Var[X,).

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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Let (X,} be a sequence of rv's such that X, is distributed as Z with probability pPn and as onZ with probability 1 – Pn where Z- N(0, 1), pn →pe [0, 1] and on → o. |(a) Show that X, x if and only if p = 1. What is the distribution of X? (b) lim,- Var[X„] is not necessarily the same as Var[X]. Find the possible values of lim,- Var[X,).
Transcribed Image Text:Let (X,} be a sequence of rv's such that X, is distributed as Z with probability pPn and as onZ with probability 1 – Pn where Z- N(0, 1), pn →pe [0, 1] and on → o. |(a) Show that X, x if and only if p = 1. What is the distribution of X? (b) lim,- Var[X„] is not necessarily the same as Var[X]. Find the possible values of lim,- Var[X,).
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