(I'm not sure whether this thread belongs in Pre- or the Uni forum)

How can we prove that for a discrete probability distribution $\displaystyle D = <d_1, d_2, ..., d_n>$

$\displaystyle \sum_{i=1}^n P(D=d_i)=1$

using the axioms of probability.

---------

My start:

We know that $\displaystyle 0\le \sum_{i=1}^n P(D=d_i)\le n$ since $\displaystyle 0\le P(D = d_i) \le 1 \quad \forall i$

but then what?