Inn - nah) Jimmy bought a magic ant: It walks along the real line (oo,oo) as a standard Brownian motion; its position at time t is B(t ), t I_> 0, B (0) 0. Give your answers as @(3: )2 P(Z <_: for the correct :1: where z denotes a standard unit normal n what is probability that ant 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 con- cluded that the ant's position follows X (t) : 230:) t + 10, t 2 0. What is the probability that the ant is on the positive axis (> 0) at time t : 9