Maximum likelihood estimators A Model for Genotypes 2 puntos posibles (calificables) In a simple model of inheritance, a given person has genotypes AA, aa or Aa. Each person has two alleles (each of which is either a or A), and the first and the second allele are inherited independently and are identically distributed. Note that Aa is the same as aA: the order of alleles does not matter. Therefore P (AA) = 02, \\P (aa) = (1 - 0) where 0 e (0, 1) is an unknown parameter. 1) What is P (Aa) in terms of 0? P (Aa) = 2* theta * (1-theta) 2 . 0 . (1 - 0) 2) Define the random vector X = {0, 1} associated to a random person with genotype g by (1, 0, 0) ifg = AA X = (0, 1,0) ifg = aa (0, 0, 1) ifg = Aa What is the pmf p (x) of X for a = (21, 2, 23) E {(1, 0, 0) , (0, 1, 0) , (0, 0, 1) }? O p(z) = (0)201 (1 - 0)202 [20 (1 - 0)123 Op(x) = (0) 23 (1 - 0)221 120 (1 - 0) 1202 O p(x) = 0" (1 - 0) 1-2 O p (2) = (02) 21 (1 - 02) 202 (1-20) 23 O p(x) = (1-0)201 (0) 2:2 (120 (1-0) 1203