E(X) = ∑ n⋅P(X=n)
= P(X=1) + P(X=2)+P(X=2) + P(X=3)+P(X=3)+P(X=3) + P(X=4)+P(X=4)+P(X=4)+P(X=4) + ...
= p1+2p2+3p3+4p4+5p5+6p6+⋯
=Pr(X>0)+p2+2p3+3p4+4p5
=Pr(X>0)+Pr(X>1)+p3+2p4+3p5+⋯
=Pr(X>0)+Pr(X=1)+Pr(X=2)+p4+2p5+⋯
= ∑P(X>=n)
Hence, proved
Let X be a random variable that only takes the values 0,1,2, 3, 4, .. Prove...
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