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$X$ is normal with $E[X]=-1, Var(X)=4$, $Y$ is esponential with $E[Y]=1$, they are independent, if $T=pXY+q$ with $p, q \in R$, what is $Var(T)$, I get $E[T]=q-p$ and $Var(T)=p^2(E[X^2]E[Y^2]-(E[X])^2(E[Y])^2)=$?

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Hint: For any random variable $Z$: $$ {\rm E}[Z^2]=\mathrm{Var}(Z)+{\rm E}[Z]^2. $$ Use this to find ${\rm E}[X^2]$ and ${\rm E}[Y^2]$.

Stefan Hansen
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