Does anyone know exact sampling distribution (or moments) of the intercept term with stochastic regressors?

Question

When regressors are stochastic, the exact sampling distribution of the parameters of the regression equation are not known for the cases of more than 2 regressors. However for the case of 2 regressos, the exact sampling distribution of the slope parameter is known to follow the Beta distribution under parent normality, but the distibution of the intercept still seems to be unknown. Does anyone know about the exact distribution of the intercept in 2 regressor case? And know about distributions of the regressor parameters for the general case with more than 2 regressors?

Answer 1

no