1. The problem statement, all variables and given/known data
If ##X## is any random variable defined on ##[0,\infty]## with continuous CDF ##F_X(t)##. Prove that ##E(X)=\int_1^\infty (1-F_X(t)) dt##.
.
2. Relevant equations
3. The attempt at a solution
I am not sure how to go about this. I think double integration can be used to prove it, but I don't want to go down that path. Is there another which I can prove this. Thanks.
If ##X## is any random variable defined on ##[0,\infty]## with continuous CDF ##F_X(t)##. Prove that ##E(X)=\int_1^\infty (1-F_X(t)) dt##.
.
2. Relevant equations
3. The attempt at a solution
I am not sure how to go about this. I think double integration can be used to prove it, but I don't want to go down that path. Is there another which I can prove this. Thanks.
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