Obtain a closed-form solution (Expected value and Variance of the short rate ) of the Vasicek Model by trying to express the short rate r at a future time s from a known time t. To begin with, gather all the rate-dependent terms to the left-hand side.

a) Show that the Expected value becomes

b) And Variance becomes

c) What are the long term values of the above-expected value and the variance of the short rate, i.e.