Consider the univariate multiple regression model y | x = Bo + B x + + Bpxip + 24;. i = 1,....n. where y, denotes yield for a crop in year i, x, denotes the observed value of explanatory variable j during year i, u, denotes a disturbance term in year i,=(B): (p+1) x 1 is a vector of coefficients to be estimated, and x=(X) is a vector of observed explanatory variables during year i. Assume the us are independent N(0, 2). Introduce a vague prior for (.0).

(a) Find the joint posterior density for (B. ).

(b) Find the marginal posterior density for (B).

(e) Find the marginal posterior density for ().

(d) Find the marginal posterior density for (B1).

(e) Find the predictive density for a new observation y*, based upon a new observation vector x* = (x)).