The random variables xi n left begin array l n x text with probability frac 1 2 n alpha text with probability frac 1 2 end array ight are independent Prove that for ( alpha frac 1 2 ) the Lyapunov theorem may be applied to them ...

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The random variables [ xi_{n}=left{begin{array}{l} -n^{x} text { with probability } frac{1}{2} +n^{alpha} text { with

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The random variables

\[ \xi_{n}=\left\{\begin{array}{l} -n^{x} \text { with probability } \frac{1}{2} \\ +n^{\alpha} \text { with probability } \frac{1}{2} \end{array}\right. \]

are independent. Prove that for $\alpha>-\frac{1}{2}$ the Lyapunov theorem may be applied to them

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Theory Of Probability

ISBN: 9781351408585

6th Edition

Authors: Boris V Gnedenko

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Question Posted: May 06, 2024 04:02 AM

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The random variables [ xi_{n}=left{begin{array}{l} -n^{x} text { with probability } frac{1}{2} +n^{alpha} text { with

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Theory Of Probability

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