Question #341705



1. X1,,XniidN(0,1).X_1,\ldots,X_n \sim iid \sim N(0,1). Define Xˉ\bar{X} (sample mean) and S2=1nXi2S^2=\sum_1^n X_i^2 .


a) Show that Xˉ\bar{X} and S2S^2 are dependent.


b) Derive the conditional distribution of Xˉ\bar{X} , given S2S^2.


c) Determine c(u) such that P[Xˉ\bar{X} > c(u)|u] =alpha, where u=S2\text{u}=S^2.


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