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Question 3 Consider a sequence of random variables X1, X2,.. Suppose X follows a discrete distri- bution taking two possible values {0, n²}, with P(X,=0) = 1 – and P(X, = n²) = . (а) Calculate E(Xn). What happens to E(Xn) as n → 0? (b) Does X, converge in probability to some real number? If so, find that number and prove. If not, explain.

Question 3 Consider a sequence of random variables X1, X2,.. Suppose X follows a discrete distri- bution taking two possible values {0, n²}, with P(X,=0) = 1 – and P(X, = n²) = . (а) Calculate E(Xn). What happens to E(Xn) as n → 0? (b) Does X, converge in probability to some real number? If so, find that number and prove. If not, explain.

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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Question 3 Consider a sequence of random variables X1, X2,.... Suppose X follows a discrete distri- bution taking two possible values {0, n²}, with P(X,=0) = 1 – and P(X, = n²) = !. (а) Calculate E(Xn). What happens to E(Xn) as n → 0? (b) and prove. If not, explain. Does X, converge in probability to some real number? If so, find that number
Transcribed Image Text:Question 3 Consider a sequence of random variables X1, X2,.... Suppose X follows a discrete distri- bution taking two possible values {0, n²}, with P(X,=0) = 1 – and P(X, = n²) = !. (а) Calculate E(Xn). What happens to E(Xn) as n → 0? (b) and prove. If not, explain. Does X, converge in probability to some real number? If so, find that number
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