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This is a continuous probability exercise which is pretty simple but when I got to part C I was doing the normal integration and I got it wrong because I used X to find the expected value of X instead of absolute (X) . Now I'v been taking this course for 3 months and this is the first time I see absolute (X) , why did they use it ?

Mike Harb
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    The expectation exists when the integral is absolutely convergent, hence the absolute value. However, to get the value of the expectation, remove the absolute value. – Jean-Claude Arbaut Mar 28 '16 at 10:07
  • Random variable with Cauchy distribution doesn't have moments. https://en.wikipedia.org/wiki/Cauchy_distribution – K.K.McDonald Mar 28 '16 at 10:10
  • Does absolutely convergent has to do with the need to check that we aren't find the mean of an infinite left part with an infinite right part (by right and left I mean the positive axis and the negative axis) , as if we are finding the difference of two infinities , right ? But it turned out that even thought each part is infinitely far , the mean is 0 , how come , and can you give an example ? – Mike Harb Mar 28 '16 at 10:28
  • "the mean is 0" The mean of what? Please be specific (if you try to be, you should see the problem right away). – Did Mar 28 '16 at 11:30
  • The mean of the random variable X – Mike Harb Mar 28 '16 at 12:02
  • http://math.stackexchange.com/questions/60766/what-is-the-result-of-infinity-minus-infinity – Alex Mar 28 '16 at 12:10
  • "The mean of the random variable X" No. – Did Mar 31 '16 at 12:04

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