7.2 Assume the data in Example 7.1 are missing always completely at random

(MACAR). By first conditioning on ( y11,…, yn1), find the exact small-sample variance of ????̂2. (Hint: If u is chi-squared on d degrees of freedom, then E(1/u) = 1/(d−2)) (seeMorrison 1971). Hence show that

????̂2 has a smaller sampling variance than y2 if and only if ????2 >1/(r−2), where r is the number of completely observed units.