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A conditional expectation is the expectation of a random variable, given information on another variable or variables (mostly, by specifying their value).

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Expected value of q given y is weighted average of mean q and and y

It is assumed that: 1) $y=q+u$ Where $q$ is productivity and $y$ a testscore that measures true productivity. $u$ is a normally distributed error term, independent of $q$, with zero mean and con …
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