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Sep 20th, 2014
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  1. documentclass[10pt]{article}
  2. usepackage{mathtools}
  3. usepackage{amsthm} %for proof
  4.  
  5. begin{document}
  6.  
  7. begin{alignat}{3}
  8. E(epsilon)&=E_{X}(E(epsilon|X))=E_{X}(0)=0 &\
  9. V(epsilon)&=E_{X}(V(epsilon|X))+V_{X}(underbrace{E(epsilon|X)}_text{$=0$}) &=E_{X}(V(epsilon|X))+0\
  10. & &=E(sigma^{2}_{Y|X))
  11. end{alignat}
  12.  
  13.  
  14. begin{align}
  15. E(epsilon)&=E_{X}(E(epsilon|X))=E_{X}(0)=0 &\
  16. V(epsilon)&= begin{split} E_{X}(V(epsilon|X))+V_{X}(underbrace{E(epsilon|X)}_text{$=0$}) &&=E_{X}(V(epsilon|X))+0\
  17. &&=E(sigma^{2}_{Y|X)) end{split}
  18. end{align}
  19.  
  20. begin{align}
  21. E(epsilon)&=E_{X}(E(epsilon|X))=E_{X}(0)=0 &\
  22. V(epsilon)&= E_{X}(V(epsilon|X))+V_{X}(underbrace{E(epsilon|X)}_text{$=0$}) &&=E_{X}(V(epsilon|X))+0\
  23. &&=E(sigma^{2}_{Y|X))
  24. end{align}
  25.  
  26. end{document}
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