Jimmy bought a magic ant: It walks along the real line,(-,), as a standard Brownian motion; its position at time t is B(t), t0, B(0) = 0. Give your answers as (x) =P(Zx), for the correct x, where Z denotes a standard unit normal N(0,1).YOU MUST SHOW YOUR WORK.

(a) What is the probability that the ant is above (>) +3 at time t= 9?

(b) Given that the ant is at position-1.5 at time t= 5, what is the probability that the ant is above (>) +3 at time t= 9?

(c) What is the probability that the ant will reach position-5 before reaching+7?

(d) The ant drank a taste of Jimmy's father's Martini after which Jimmy concluded that the ant's position follows X(t) = 2B(t)-t+ 10, t0. What is the probability that the ant is on the positive axis (>0) at time t= 9?