Want to know the detail of how to differential those questions using Brownian motion and Ito Process to satisfy them.

1. Let Wt be a Brownian motion and Rt be an Ito process satisfying the stochastic differential equation dRt = (8 - 2Rt) dt + 5dWt, Ro = 1. (The process Rt is used to model the spot interest rate in the Vasicek interest rate model. ) (a) Use Ito formula to calculate d (e2t Put). (b) Integrate the equation to find Rt = 4 - 3e-2t + 5e-2t e 2s dW s - O (c) Find E[R.] and Var( Rt). What is the distribution of Rt