The Shannon index (sometimes called the Shannon-Wiener index or Shannon-Weaver index) is
Chapter 9, Problem 37(choose chapter or problem)
The Shannon index (sometimes called the Shannon-Wiener index or Shannon-Weaver index) is a measure of diversity in an ecosystem. For the case of three species, it is defined as H 2p1 ln p1 2 p2 ln p2 2 p3 ln p3 where pi is the proportion of the ecosystem made up of species i. (a) Express H as a function of two variables using the fact that p1 1 p2 1 p3 1. (b) What is the domain of H? (c) Find the maximum value of H. For what values of p1, p2, p3 does it occur?
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