Suppose that X₁, X2, ka)=P(X = _k) =1/2. Let Yn = Xn = n 2 Xi. are independent, such that, for each k ≥ 1, P(Xk = i) Use Chebyshev's inequality to show that, if a ≤ 0, then Y₁ ²0. ii) Does Yn still converge in probability if a = 1?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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Suppose that X₁, X2,
k^)=P(Xk =_ka) =1/2. Let Yn = X = n 2 Xi.
N
n
are independent, such that, for each k ≥ 1, P(Xk =
i) Use Chebyshev's inequality to show that, if a ≤ 0, then Y₂²0.
ii) Does Yn still converge in probability if a = 1?
Transcribed Image Text:Suppose that X₁, X2, k^)=P(Xk =_ka) =1/2. Let Yn = X = n 2 Xi. N n are independent, such that, for each k ≥ 1, P(Xk = i) Use Chebyshev's inequality to show that, if a ≤ 0, then Y₂²0. ii) Does Yn still converge in probability if a = 1?
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