An animal population has N species, with population proportion ? i of species i. Simpson?s index of
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An animal population has N species, with population proportion ?i of species i. Simpson?s index of ecological diversity (Simpson 1949) is I(?) = 1 ? ??i2. [Rao (1982) surveyed diversity measures.]
a. Two animals are randomly chosen from the population, with replacement. Show I(?) is the probability they are different species.
b. For proportions p for a random sample, show that the estimated asymptotic standard error of I(p) is
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