Suppose, that, for constants a and b, E[YlX] = a + bX Show that b = Cov(X,Y)/Var(x)
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Remember $\displaystyle {\rm Cov}(X,Y)=E[XY]-E[X]E[Y]$. Use $\displaystyle E[XY]=E[X E[Y|X]]$ and $\displaystyle E[Y]=E[E[Y|X]]$, substitute $\displaystyle E[Y|X]=a+bX$ and check that you get $\displaystyle b\,{\rm Var}(X)$.
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