Regressing with zero covariance

EasyRandom Variables Statistics~3m

Random variables $X$ and $Y$ satisfy $E[X] = 6$ , $V[X] = 2$ , $E[Y] = 8$ , $V[Y] = 10$ , and $\operatorname{Cov}(X, Y) = 0$ . You fit a simple linear regression predicting $Y$ from $X$ , obtaining $\hat Y = aX + b$ . What is $a + b$ ?

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Slope $a=\operatorname{Cov}(X,Y)/V[X]$ . What is it when $\operatorname{Cov}=0$ ?
$a=0$ , and $b=E[Y]-a\,E[X]=8$ , so $a+b=8$ .

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Regressing with zero covariance

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