The article Feeding Ecology of the Red-Eyed Vireo and
Chapter 14, Problem 14.14(choose chapter or problem)
The article Feeding Ecology of the Red-Eyed Vireo and Associated Foliage-Gleaning Birds (Ecological Monographs, 1971: 129152) presents the accompanying data on the variable X the number of hops before the first flight and preceded by a flight. The author then proposed and fit a geometric probability distribution [p(x) P(X x) px1 q for x 1, 2, . . . , where q 1 p] to the data. The total sample size was n 130. a. The likelihood is (px11 q) (pxn1 q) pxin qn . Show that the mle of p is given by p (xi n)/xi , and compute p for the given data. b. Estimate the expected cell counts using p of part (a)[expected cell counts n ( p)x1 q for x 1, 2, . . . ],and test the fit of the model using a 2 test by combiningthe counts for x 7, 8, . . . , and 12 into one cell (x 7).
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