1. Obtain a closed form solution (Expected value and Variance of the short rate r) of Vasicek Model {dr_t= (-r_t )dt + dW_t } 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.

   1. Show that the Expected value becomes + (r_t-) e^(-(s-t) )

   2. And Variance becomes ^2/2 [1-e^(-2(s-t) ) ]

   3. What are the long term values of the above expected value and the variance of the short rate, i.e. s