Please answer the following questions, justifying your answers: a. Suppose Bt is a Brownian motion. Is the stochastic process Y; = 2 +t+eB a martingale? b. The risk-free interest rate rt in the Vasicek model follows the Ornstein- Uhlenbeck process. It is known that rt can be expressed as a stochastic integral rt = 0.03+ (ro - 0.03) e =0.8t +0.002e - 0.8t 0.88 dB, where B is a Brownian motion. Find the distribution of rt as of time 0. Please answer the following questions, justifying your answers: a. Suppose Bt is a Brownian motion. Is the stochastic process Y; = 2 +t+eB a martingale? b. The risk-free interest rate rt in the Vasicek model follows the Ornstein- Uhlenbeck process. It is known that rt can be expressed as a stochastic integral rt = 0.03+ (ro - 0.03) e =0.8t +0.002e - 0.8t 0.88 dB, where B is a Brownian motion. Find the distribution of rt as of time 0