Cauchy distributed random variables

Reference no: EM131832989

The law of large numbers does not hold for Cauchy distributed random variables. Let X₁, X₂,......., X_n be a sequence of independent identically distributed random variables with probability density functions fx_n(x) = [π(1 + x²)]^-1. Show that no finite constant m exists to which the sample means (X₁ + ... + X_n)/n converge in probability.

Reference no: EM131832989

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