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- documentclass[10pt]{article}
- usepackage{mathtools}
- usepackage{amsthm} %for proof
- begin{document}
- begin{alignat}{3}
- E(epsilon)&=E_{X}(E(epsilon|X))=E_{X}(0)=0 &\
- V(epsilon)&=E_{X}(V(epsilon|X))+V_{X}(underbrace{E(epsilon|X)}_text{$=0$}) &=E_{X}(V(epsilon|X))+0\
- & &=E(sigma^{2}_{Y|X))
- end{alignat}
- begin{align}
- E(epsilon)&=E_{X}(E(epsilon|X))=E_{X}(0)=0 &\
- V(epsilon)&= begin{split} E_{X}(V(epsilon|X))+V_{X}(underbrace{E(epsilon|X)}_text{$=0$}) &&=E_{X}(V(epsilon|X))+0\
- &&=E(sigma^{2}_{Y|X)) end{split}
- end{align}
- begin{align}
- E(epsilon)&=E_{X}(E(epsilon|X))=E_{X}(0)=0 &\
- V(epsilon)&= E_{X}(V(epsilon|X))+V_{X}(underbrace{E(epsilon|X)}_text{$=0$}) &&=E_{X}(V(epsilon|X))+0\
- &&=E(sigma^{2}_{Y|X))
- end{align}
- end{document}
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