Le Cam's Inequality

Let  be the sum of  random variates  with a Bernoulli distribution with . Then

where

REFERENCES:

Le Cam, L. "An Approximation Theorem for the Poisson Binomial Distribution." Pacific J. Math. 10, 1181-1197, 1960.

Le Cam, L. "On the distribution of Sums of Independent Random Variables." In Bernoulli, Bayes, Laplace: Proceeding of an International Research Seminar (Ed. J. Neyman and L. M. Le Cam). New York: Springer-Verlag, pp. 179-202, 1963.

Steele, J. M. "Le Cam's Inequality." Amer. Math. Monthly 101, 48-54, 1994.