(i) If X n , n 1, 2, brvbar , are independent r v s defined on the probability space ( Icirc copy , A , P ), show that If and only if For every Icirc micro 0 (ii) Reconcile this result with the result in Exercise 4 in Chapter 3 a s Xn 0 00...

For an arbitrary but fixed 0 set An Xn Independence of Xns implies independence of Ans n 1 Then ...

(i) If X n , n = 1, 2,¦, are independent r.v.s defined on the probability space...

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(i) IfX_n,n= 1, 2,€¦, are independent r.v.s defined on the probability space (Î©,A,P), show that

a.s. Xn → 0 п>00

If and only if

For every Îµ > 0.

(ii) Reconcile this result with the result in Exercise 4 in Chapter 3.

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An Introduction to Measure Theoretic Probability

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Authors: George G. Roussas

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(i) If X n , n = 1, 2,¦, are independent r.v.s defined on the probability space...

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a.s. Xn → 0 п>00

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An Introduction to Measure Theoretic Probability

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