Robbins lemma

Robbins lemma

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

: operatorname{E}(X f(X - 1)) = lambda operatorname{E}(f(X)). ,

Robbins introduced this proposition while developing empirical Bayes methods.


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