Sometimes, a statistician might want to model what happens when X is measured in a noisy way. Suppose U X is a "white noise" random variable that has the following properties: U X is independent of both X and Y; E [ ] = 0 E[U X ]=0; V [ ] > 0 V[U X ]>0. Let ~ X be a random variable that is the sum of X and U X . That is, ~ = X =X U X . Intuitively, you might think of ~ X as a "noisy" measurement of X. Let ~ Y X be the slope of the BLP for Y given the noisy measurement ~ X ~ . Show that ~ Y X YX . (Intuitively, a relationship appears weaker when there is measurement error in X)