Exercise 3: Let (Yn)neN be a sequence of random variables with the property -a < Y, < 0 for a constant a, 0 < a < 0, and Ym < Yn for Vm < n. i) Why does the Monotone Convergence Theorem for (Y)nEN not hold? ii) Show that lim E[Y,] = E[ lim Y,]. n-00

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A: Given that

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A: Note: According to the Bartleby guidelines expert solve only one question and rest can be reposted.

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A: answer is in next step

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A: Note: According to Bartleby guidelines; for more than one question asked, only the first one is to…

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A: Xn→X in LpΩ, ℙ.EXn-Xp→0, p≥1.

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A: Given::- 26. (Barndorff-Nielsen) Suppose (En) is a sequence of events such that lim P(En) = 0,…

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A: We will get the conclusion by using the definition of a conditionally Convergent Series.  Option (b)…

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A: Solution a: Given that fn(x)=11+(nx+1)3 in 0,1. Now, f(x)=limn→∞fn(x)=limn→∞11+(nx+1)3=0,    x≠012,…

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A: 17. I. is true.

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A: Let the sum of the series be given by Sn. ⇒Sn=∑n=0∞tan-1(x)x2+n2ln (n+2) un=∑ n=0∞tan-1(x)x2+n2ln…

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A: