7.9 Exercises on Chapter 7
1. Show that in any experiment E in which there is a possible value y for the random variable such that , then if z is any other possible value of , the statistic t=t(x) defined by is sufficient for θ given x. Hence, show that if is a continuous random variable, then a naïve application of the weak sufficiency principle as defined in Section 7.1 would result in for any two possible values y and z of .
2. Consider an experiment . We say that censoring (strictly speaking, fixed censoring) occurs with censoring mechanism g (a known function of x) when, instead of