The data below are the numbers of females and males in the progeny of 16 female...

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The data below are the numbers of females and males in the progeny of 16 female light brown apple moths in Muswellbrook, New South Wales, Australia (from Lewis, 1987). (a) Calculate the proportion of females in each of the 16 groups of progeny. (b) Let Y, denote the number of females and n, the number of progeny in each group (i variables each with the binomial distribution 1, ., 16). Suppose the Y,'s are independent random w:0) = () om (1 – ey, %3D Find the maximum likelihood estimator of 0 using calculus and evaluate it for these data. (c) Use a numerical method to estimate 0 and compare the answer with the one from (b). Table 1.4 Progeny of light broun apple moths. Progeny Females Males group 18 11 31 22 3 34 27 4 29 24 29 28 25 8. 26 9. 38 10 12 14 11 19 23 12 31 13 14 20 14 4 34 15 16 7. 12 The data below are the numbers of females and males in the progeny of 16 female light brown apple moths in Muswellbrook, New South Wales, Australia (from Lewis, 1987). (a) Calculate the proportion of females in each of the 16 groups of progeny. (b) Let Y, denote the number of females and n, the number of progeny in each group (i variables each with the binomial distribution 1, ., 16). Suppose the Y,'s are independent random w:0) = () om (1 – ey, %3D Find the maximum likelihood estimator of 0 using calculus and evaluate it for these data. (c) Use a numerical method to estimate 0 and compare the answer with the one from (b). Table 1.4 Progeny of light broun apple moths. Progeny Females Males group 18 11 31 22 3 34 27 4 29 24 29 28 25 8. 26 9. 38 10 12 14 11 19 23 12 31 13 14 20 14 4 34 15 16 7. 12

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