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I know that the sample mean converges to population mean with convergence rate $\frac{1}{\sqrt{n}}$.

How can we prove this?

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    @Phira Having taught probability theory to undergraduates for close to forty years, let me assure that _many_ students who claim to "know" things about convergence in probability theory (because they have copied it down from the blackboard or read it in their textbooks) would be hard put not just to distinguish between the various forms of convergence but even to state correctly, even after prompting and gentle nudging, the definition of a convergent sequence of real numbers. There is no point answering this question unless the OP reveals _something_ about the level of his knowledge.2012-11-04

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