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February 21st, 2011, 07:45 AM  #1 
Member Joined: Dec 2010 From: Drachten, the Netherlands Posts: 49 Thanks: 0  moments of Cauchy distribution
show that for a Cauchy distribution the first moment and second moment about the origin does not exist. a Cauchy distribution has the following distribution: f(x) = (B/pi)/((xa)^2+b^2) for infinity<x< infinity I tried to find E(X)= integral from infinity to infinity of x(B/pi)/((xa)^2+b^2) and E(X^2)= integral from infinity to infinity of x^2(B/pi)/((xa)^2+b^2) However the integral is to hard for me to solve. Can someone help me with this or is there some other method to prove that these moment does not exists? Thanks in advance 
February 21st, 2011, 05:15 PM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: moments of Cauchy distribution
Setting a=0 and ignoring the 1/pi factor: Let u = x²+b², du = 2x dx which doesn't exist. Break the integrals in half and use substitutions to simplify them. 

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