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 Unnumbered Display Equation 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

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