2. Let \\( X \\) and \\( Y \\) be two arbitrary random variables. Define the conditional variance of \\( X \\) given \\( Y \\) by \\[ \\operatorname{Var}[X \\mid Y]=\\mathbb{E}\\left[X^{2} \\mid Y\ ight]-(\\mathbb{E}[X \\mid Y])^{2} . \\] Show that \\( \\operatorname{Var}[X \\mid Y] \\geq 0 \\) and the variance decomposition formula \\[ \\operatorname{Var}[X]=E[\\operatorname{Var}[X \\mid Y]]+\\operatorname{Var}[E[X \\mid Y]] \\]