(Solved): 6. If \( X \) and \( Y \) are independent and identically distributed (iid) w ...

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6. If \( X \) and \( Y \) are independent and identically distributed (iid) with mean \( \mu \) and variance \( \sigma^{2} \), find \[ E\left[(X-Y)^{2}\right] \] 7. If \( E X=1 \) and \( \operatorname{Var}(X)=5 \), find (a) \( E\left[(2+X)^{2}\right] \) (b) \( \operatorname{Var}(4+3 X) \)