An article on the feeding ecology of certain types of birds 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) = p*-1. g for x = 1, 2, ..., where g = 1 - p) to the data. The total sample size was n = 125. 2 3 4 5 6 78 9 10 11 12 Number of Times x Observed 48 31 20 7 5 4 3 2 1 1 2 1 E* - n) (a) The likelihood is (p*1 -1. g) ..... (p*n-1. g) = px; -n.d". Show that the mle of p is given by p = Cx; -n) We wish to maximize pDx; -n.g° or (5x; - n) In Equating d/dp to 0 yields Solving for p results in p = Σ Compute p for the given data. (Round your answer to three decimal places.) (b) Estimate the expected cell counts using p of part (a) [expected cell counts = n. (p)* -1. ĝ for x = 1, 2, ...]. Combine the counts for x = 7, 8, ..., and 12 into one cell (x 2 7). (Round your answers to one decimal place.) 1 2 3 4 5 6 27 Observed Counts 48 31 20 7 5 4 10 Expected Counts Test the fit of the model using x2 test with a significance level of 0.05. Calculate the test statistic. (Round your answer to two decimal places.)