Sunday, 4 May 2014

probability theory - Understanding inticnfty(xc)dF(x) through integration by parts

Following this answer, it is claimed that we can solve the problem in the following way:



c(xc)dF(x)=limy(yc)F(y)cF(x)dx.



where F is the cumulative distribution function of a given random variable.



Does this limit exist though? In my understanding, since distribution function saturates at 1, the first limit should converge to infinity? What am I missing?

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