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[Solved] (a) If X and Y are independent random variables, var;(X)=4, and var;(Y)=3, find var;(-X-2Y+3). (4 points) (b) Show that E[ (X-μ)^2 ]=E(X^2)-μ

Question: (4 points) (a) If X and Y are independent random variables, $\operatorname{var}\left( X \right)=4$, and $\operatorname{var}\left( Y \right)=3$, find $\operatorname{var}\left( -X-2Y+3 \right)$.

(4 points) (b) Show that $E\left[ {{\left( X-\mu \right)}^{2}} \right]=E\left( {{X}^{2}} \right)-{{\mu }^{2}}$, where µ:= E[X].

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[Solved] (a) If X and Y are independent random variables, var;(X)=4, and var;(Y)=3, find var;(-X-2Y+3). (4 points) (b) Show that E[ (X-μ)^2 ]=E(X^2)-μ

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