Robbins lemma
From HandWiki
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]
- [math]\displaystyle{ \operatorname{E}(X f(X - 1)) = \lambda \operatorname{E}(f(X)). }[/math]
Robbins introduced this proposition while developing empirical Bayes methods.
References
- ↑ Samaniego, Francisco J. (2015), Stochastic Modeling and Mathematical Statistics: A Text for Statisticians and Quantitative Scientists, CRC Press, p. 118, ISBN 9781466560475, https://books.google.com/books?id=v1HSBQAAQBAJ&pg=PA118.
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