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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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