Let, Xk k = 1, 2, 3¦ be a sequence of IID Cauchy random variables with and
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and let Sn be the sequence of sample means,
(a) Show that also follows a Cauchy distribution.
(b) Prove that in this case, the sample mean does not converge in probability and therefore the weak law of large numbers does not apply. What assumption has been violated in this case that makes the weak law of large numbers not applicable?
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Related Book For
Probability and Random Processes With Applications to Signal Processing and Communications
ISBN: 978-0123869814
2nd edition
Authors: Scott Miller, Donald Childers
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