Let the r v s Xj, j yen 1, be distributed as follows Show that the Lindeberg condition (relation (12 24)) holds, if and only if Icirc plusmn 3 2 Conclude that For Icirc plusmn 3 2, show that which is implied by n 2a Eacute 2 s n 2 for large n, so that g n ( Eacute ) 0 Next, g n ( Eacute ) yen 1 Eac...

Here X j 0 2 j 2 X j X 2 j 2j 2 6j 21 13 j 2 so that s 2 n nn12n118 Consider js with j 1 ...

Let the r.v.s Xj, j ¥ 1, be distributed as follows: Show that the Lindeberg condition (relation

Question:

Let the r.v.s Xj, j ‰¥ 1, be distributed as follows:

1 1 P(X; = ± jª) = a > 1. P(X; =0) = 1 – 6j2(a-1)' %3D 3 j2(a-1) '

Show that the Lindeberg condition (relation (12.24)) holds, if and only if Î± < 3/2. Conclude that

For Î± < 3/2, show that

which is implied by n^2a < É›²s_n² for large n, so that g_n (É›) = 0. Next,

g_n(É›) ‰¥ 1 - É›²/18 (l €“ 1/k)(2- 1/k) k^2a/É›²s_n² k^3-2a,

Where k = [(É›s_n)^l/Î±], and conclude that the expression on the right-hand side does not converge to 0 for Î± ‰¥ 3/2.

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An Introduction to Measure Theoretic Probability

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Authors: George G. Roussas

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Let the r.v.s Xj, j ¥ 1, be distributed as follows: Show that the Lindeberg condition (relation

Question:

1 1 P(X; = ± jª) = a > 1. P(X; =0) = 1 – 6j2(a-1)' %3D 3 j2(a-1) '

Step by Step Answer:

Here X j 0 2 j 2 X j X 2 j 2j 2 6j 21 13 j 2 so that s 2 n nn12n118 Consider js with j 1 ...View the full answer

An Introduction to Measure Theoretic Probability

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