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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

\begin{displaymath}
\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,
\end{displaymath}

where

\begin{displaymath}
\lambda\equiv \sum_{i=1}^n p_i.
\end{displaymath}

See also Bernoulli Distribution


References

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




© 1996-9 Eric W. Weisstein
1999-05-26