Question: $underline{text Exercise 5: })$ Let $mathrm{X}$ and $mathrm{Y}$ are independent random variables with $mathrm{E}mathrm{X])=mathrm{E} (mathrm{Y})=05. Show that $$ operatorname Var) (XY)=operatorname Var}(X) operatornate Var}(Y) $$

$\underline{\text Exercise 5: })$ Let $\mathrm{X}$ and $\mathrm{Y}$ are independent random variables with $\mathrm{E}\mathrm{X])=\mathrm{E} (\mathrm{Y})=05. Show that $$ operatorname Var) (XY)=\operatorname Var}(X) \operatornate Var}(Y) $$ $\underline[\text Exercise 6: 33$ If the joint probability density function of $X$ and $y$ is $$ f(x, y)=\left\{\begin{array}{11} 1 & \text { if ) 0
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