Robbins lemma

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In statistics, the Robbins lemma, named after Herbert Robbins, states that if X is a random variable having a Poisson distribution with parameter λ, and f is any function for which the expected value E(f(X)) exists, then[1]

E⁡(Xf(X−1))=λE⁡(f(X)).

Robbins introduced this proposition while developing empirical Bayes methods.

References

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  1. ↑ Script error: No such module "citation/CS1"..

Script error: No such module "Check for unknown parameters".

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