Show that sn also follows a cauchy distribution

Reference no: EM131216288

Let be a sequence of IID Cauchy random variables with

(a) Show that s_n 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?

Reference no: EM131216288

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