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Almost Sure Convergence of Rayleigh Distributed Random Variables

A simple calculation tells us that $$\mathbb{P}( X_1 > x ) = e^{ - x^2/2}.$$ It follows that $$\mathbb{P}( X_n > 1/\sqrt{n} ) = \mathbb{P}( X_1 > \sqrt{n} ) = e^{ - n/2}.$$ In particular, $$\...
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