Consider the regression model Yt = 0 + 1Xt + ut, where ut follows the stationary AR(1) model with mean 0 and variance a. Suppose

Consider the regression model Yt = β0 + β1Xt + ut, where ut follows the stationary AR(1) model

with mean 0 and variance

a. Suppose that Xt is independent of uj for all t and j. Is Xt exogenous (past and present)? Is Xt strictly exogenous (past, present, and future)?
b. Suppose that Xt = ut+1. Is Xt exogenous? Is Xt strictly exogenous?

and Idyl < 1.