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5.2.5 (Example 5.2.6 Continued) Suppose thatXY are iid having the following common distribution. PC,-1-cip.i-1. 2. 3. and 2 <p < 3 Here. c c(p) (> 0) is such that Σ | P(X,-i) = 1.. Is there a real number a = a(p) such that Xn → a as n → 00, for all fixed 2 <p < 3? FYI: Example 5.2.6 In order to appreciate the importance of Khinchines WLLN (Theorem 5.2.3). let us consider a sequence of iid random variables - 1} where the distribution of X, is given as follows: X1 values: 1 2 3 . .. i.. . Probabilities: ษ์ ธิ์ (5.2.5) 汀戒2T ...-J 13 23 33 i3 with c 2 so that 0. This is indeed a probability distribution. Review the Examples 2.3. 1-2. 3.2 as needed. We have E(Xi-среґ which is finite. However, E(X?) this infinite series is not finite. Thus, we have a situation where μ is finite but o2 is not finite for the sequence of the iid Xs. Now, in view of Khinchines WLLN, we conclude that as Xn → E(X) = μ n → 00, From the Weak WLLN, we would not be able to reach this conclusion.

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5.2.5 (Example 5.2.6 Continued) Suppose thatXY are iid having the following common distribution. PC,-1-cip.i-1. 2. 3....
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