Friday, 9 May 2014

probability - Intuitive explanation for mathbbEX=inti0nfty1F(x),dx

I can see by manipulating the expression why EX works out to be 01F(x)dx, where F is the distribution function of X, but what is an intuitive explanation for why that is true? If at each point we sum the probability P(X>x), why should we end up with the expectation?




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