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].
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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