please show your work.

Question 1 (10 points) Calculate the expected sum obtained when three fair dice are rolled. Question 2 (10 points) Suppose that {Y(t),0 S t E 1} is a Brownian motion process with variance parameter 0'2. Show that P(Y(1) > O|Y(1/2) = a) w .9213. Question 3 (5 points) Suppose that interest is continuously compounded with a rate that is changing in time. Let r(s) denote the risk free interest rate at time s 2 0. Find the present value function P(t) = exp{ f; 'r'(s)ds} if the risk free rate evolves according to r1+sr2 1+s' r(s) = where 71 and 7'2 are given positive constants