In the discussion in Example 12.4.2, note that there was one observation from the potoroo data that had a missing value. Suppose that on the 24th animal it was observed that O2 = 16.3.
(a) Write down the observed data and expected complete data log likelihood functions.
(b) Describe the E step and the M step of an EM algorithm to find the MLEs.
(c) Find the MLEs using all 24 observations.
(d) Actually, the O2 reading on the 24th animal was not observed, but rather the CO2 was observed to be 4.2 (and the O2 was missing). Set up the EM algorithm in this case and find the MLEs. (This is a much harder problem, as you now have to take expectations over the xs. This means you have to formulate the regression problem using the bivariate normal distribution.)