Consider a 2 × 2 contingency table with the cell frequencies n ij and probabilities    , for i, j = 1, Under the independence model,  and its estimator is   say (i) Obtain the expressions for   when...

Consider a 2 × 2 contingency table with the cell frequencies n_ij
and probabilities
   , for i, j = 1,

Under the independence model,
 and its estimator is
  say

(i) Obtain the expressions for
  when the independence model may not hold.

(ii) Hence, or otherwise, comment on the rationality of the test for independence based on the odds ratio in (9.4.1).

Consider the genetical data

Find the MLE of the linkage factor θ. Compute the mean and variance of the estimator, and fin out the appropriate variance stabilizing transformation.