Here the sums are done one by one sequentially for each case.
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4. Suppose that Z є R2p has a MVN distribution Nop( 12. E.). Partition Z as Z where X є Rp and Y ...
4. Suppose that Z є R2p has a MVN distribution M2p(Hs, z). Partition Z as Z- where X є Rp and Y є Rp. Denote the means of X and Y as μζ and Ily, respectively. Let μΔ As-ty. Suppose that we obtain IID data Z1, ,Zn from the underlying distribution of Z. Let a E (0,1) be a constant. (c) Describe how to construct a simultaneous confidence interval for νΤμΔ for all non- zero v є Rp when 31,...
FR2 (4+4+4 12 points) (a) Let XI, X2, X10 be a randoin sample from N(μι,σ?) and Yi, Y2, 10 , Y 15 be a random sample from N (μ2, σ2), where all parameters are unknown. Sup- pose Σ 1 (Xi X 2 0 321 (Y-Y )2-100. obtain a 99% confidence interval for σ of having the form b, 0o) for some number b (No derivation needed). (b) 60 random points are selected from the unit interval (r:0 . We want...