Suppose that (Xn) is a sequence of integer-valued random variab Show that weak convergence of Xn →Xo is equivalent to (d) n→∞

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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Weak convergence.
3. Suppose that (Xn) is a sequence of integer-valued random variables.
(d)
Show that weak convergence of Xn → Xo is equivalent to the
convergence limn→∞ P(Xn = k) = P(Xo = k) for all integers ke Z.
n→∞
Transcribed Image Text:Weak convergence. 3. Suppose that (Xn) is a sequence of integer-valued random variables. (d) Show that weak convergence of Xn → Xo is equivalent to the convergence limn→∞ P(Xn = k) = P(Xo = k) for all integers ke Z. n→∞
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