Basic Formulas in Probability Theory and Useful Identities
Yevgeny Levanzov∗
Useful identities and notions.
1. ∀p ∈ R, (1 + p) ≤ ep. Mostly used in the form of (1 − p) ≤ e−p for p ∈ [0, 1]. Thus, for t ≥ 0, we have that (1 − p)t ≤ e−tp. √ n n 2. Stirling’s approximation: n! ∼ 2πn( e ) , where the sign ∼ means that the two quan- tities are asymptotic (that is, their ratio tends to 1 as n tends to infinity).