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Suppose you have m different parameters /1, ..., Am, and you construct m (1 - a)- confidence intervals, denoted by [/j,left, /j,right] for j = 1, ..., m. It is guaranteed that each confidence interval has the (1-a)-coverage in the sense that P (uj E [Aj left, Mi,right]) = 1 - a. (a) The number of parameters that are not covered by the confidence intervals is M = En I{u; $ [/j,left, Muj,right]}. What is the expected value of M? (b) You hope all the parameters /1, ..., Mm can be covered by the m confidence inter- vals simultaneously. Mathematically, you want to construct intervals [/j ,left, /j,right] that satsify P (uj E [/j, left, Muj,right] for all j = 1, ..., m) 2 1 -a. Consider a concrete setting with i.i.d. observations X1, ..., Xn ~ N(u, Im), where u = (M1, ..., Mm)" E Rm. Apply the idea of Bonferroni correction and construct confidence intervals that satisfy the above requirement