The article feeding ecology of the red-eyed vireo and

Question

The article "Feeding Ecology of the Red-Eyed Vireo and Associated Foliage-Gleaning Birds" (Ecological Monographs, 1971: 129-152) 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

  Show that the mle of p is given by P = 5  and compute P for the given data.

b. Estimate the expected cell counts using p of part (a) [expected cell counts  and test the fit of the model using a x₂ test by combining the counts for x = 7, 8,..., and 12 into one cell (x ≥ 7)