Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 41 / 1 / d / ii / Solution

Four unsuccessful attempts have conditional probability ${\prod }_{j=1}^4{q}_j(y)$. The outcome is then unobserved, so the observed-data likelihood integrates over it:This is a probability, whereas a responder contributes a joint density in the observed outcome. The sequential response selection model keeps outcome-dependent nonresponse in the likelihood; evaluating the product at an imputed mean would not be this likelihood.