Consider a woman who must choose between two occupations (A and B) and who may or may not interrupt her work career. For simplicity, her potential work life consists of three (equally long) periods: \"young\2. Suppose that men's and women's distributions of employment across health practitioner occupations is as described in the following table. Each number in the male (female) column is the share of all men (women) employed in any health practitioner occupation that is employed in that particular occupation. Occupation Men Women Doctors 0.50 0.30 Nurses 0.10 0.60 Other 0.40 0.10 a. What is the value of the occupational dissimilarity index? b. Now suppose that the "Doctors" occupation category is disaggregated into several specialties. After this disaggregation, the occupational distributions are as shown in the following table. Occupation Men Women Pediatricians 0.05 0.11 Internal Medicine Doctors 0.10 0.03 Ob-Gyn's 0.02 0.06 Orthopedists 0.10 0.02 Gastroenterologists 0.10 0.02 Urologists 0.0 ).02 Other Doctors 0.10 0.04 Nurses 0.10 0.60 Other 0.40 0.10 Now what is the value of the occupational dissimilarity index? c. Explain intuitively why the value of the dissimilarity index changes as it does between (a) and (b). d. Find different distributions of males and females across the disaggregated doctor specialties such that the value of the dissimilarity index does not change between (a) and (b). What must be true about the distributions for this result to occur