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On a probability theory lecture I met an interesting problem:

Let f : [0;1] -> R a bounded, 3 times continously differentiable function. Calculate the following limit

[tex]n * \int_0^1 \int_0^1 ... \int_0^1 f(\frac{x_1+...+x_n}n)-f(0.5) dx_1...dx_n[/tex] while n -> infinity

Any ideas?

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# Interesting problem

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