Multiplicative Chernoff bound



Could someone give (or point me to a source for) the correct
formulation of the multiplicative chernoff bound?

More specifically I am interested in the following case:

Let X_1,...,X_n be iid random variables with Pr[X_i = 1] = 1 - Pr[X_i
= 0] = p. Let X = (X_1 + ... + X_n) / n. I'm interested in Pr[(1-d)p <
X < (1+d)p], for 0<d<1.

Cheers,
/ALiX

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