Le Cam's Identity

Let $S_n$ be the sum of $n$ random variates $X_i$ with a Bernoulli Distribution with $P(X_i=1)=p_i$. Then

$$\sum_{k=0}^\infty \left\vert{P(S_n=k)-{e^{-\lambda}\lambda^k\over k!}}\right\vert < 2\sum_{i=1}^n {p_i}^2,$$

where

$$\lambda\equiv \sum_{i=1}^n p_i.$$

See also Bernoulli Distribution

References

Cox, D. A. ``Introduction to Fermat's Last Theorem.'' Amer. Math. Monthly 101, 3-14, 1994.