Intuition behind expected value formula?

Asked Apr 15 '19 at 15:59

Active Apr 15 '19 at 15:59

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I just learned the expected value formula for a positive random variable: $E[X] = \int_0^\infty P(X>x)dx$.

I can follow the proof but I'm a little unclear as to what the intuition behind this formula is. Can someone formulate it in a more intuitive manner?

asked Apr 15 '19 at 15:59

swedishfished

See what happens in case of a random variable taking positive integer values. – user6 Apr 15 '19 at 16:02
You are integrating the probability of $X$ being large. The more likely $X$ is to be large, the larger it is on average. – Mike Earnest Apr 15 '19 at 16:02

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