问题如下，没有理解最后一问的意思，我也没查到关于这个probability limit的公式
Now suppose that you are given a model Y = β0 + β1X1 + e where E[e] = E[e · X1] = 0. However, you do not observe X1. Instead you observe X1∗ = X1 + u, where u is some measurement error with E[u] = E[u · X1] = E[u · e] = 0. Using the formula for theprobability limit of the OLS estimator of a regression of Y on X1∗, we findβˆ1 P→Cov(Y, X∗1 )/V ar(X∗1 ) .
Plugging in for Y and X1∗, rewrite Cov(Y, X1∗) (Hint: Answer should be written in termsof the variance of X1, β1, and the variance of u). Similarly rewrite V ar(X1∗).
Combining the formula for the probability limit of the OLS estimator of a regression of
Y on X1∗ and the formulas for Cov(Y, X1∗) and V ar(X1∗), rewrite the probability limit of
the OLS estimator of a regression of Y on X1∗.