Tail-sum formula
= Tail-sum formula
For nonnegative $Y$, $E[Y]=\int_0^\infty P(Y\ge t)\,dt$; for nonnegative integer $N$, $E[N]=\sum_{k\ge1}P(N\ge k)$.
= Tail-sum formula
For nonnegative $Y$, $E[Y]=\int_0^\infty P(Y\ge t)\,dt$; for nonnegative integer $N$, $E[N]=\sum_{k\ge1}P(N\ge k)$.