# Question

Consider a sequence of IID random variables, Xn n = 1, 2, 3… each with CDF FXn (x) FX (x) 1– Q (x –µ/ σ). This sequence clearly converges in distribution since FXn (x) is equal to FX (x) for all n. Show that this sequence does not converge in any other sense and therefore convergence in distribution does not imply convergence in any other form.

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