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Two random variables $X$ and $Y$ have, $?_{X}=2,?_{Y}=?1,?_{X}=1,?_{Y}=4$, and $?_{X,Y}=1/4$. Let $U=X+2Y$ and $V=2X?Y$. Find the following quantities: (a) $E[U]$ and $E[V]$; (b) $E[U_{2}],E[V_{2}],Var(U)$, and $Var(V)$; (c) $E[UV],Cov(U,V)$, and $?_{U,V}$.

Given that?x=2 ?x=1?y=?1 ?y=4?xy=14U=X+2Y , V=2X?YPart a)The expected value of random variable U is E(U)=E(X+2Y)=E(X)+2E(Y)=2?2×1=2?2=0The expected