Variance and expected value

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If we know $ mathit{E(varepsilon_1|X_1)} $ and $ mathit{E(varepsilon^2_1|X_1)} $ then we can get a $ mathit{Var(varepsilon_1|X_1)} $ as $ mathit{E(varepsilon^2_1|X_1)} - mathit{E(varepsilon_1|X_1)}^2 $.

And conditional variance can be get as $ mathit{Var(varepsilon_1)} = mathit{Var(mathit{E(varepsilon^2_1|X_1)})} + mathit{E(mathit{Var(varepsilon_1|X_1)})} $.