Consider an insect that starts ying from the origin at time 0. At time 1, it ies to the random point (X1, Y1). Starting from this point as the origin, it ies to a random point (X2, Y2), and so on. (i) Consider the coordinates of the y at time a relative to its position at time 0. Assuming that a = 100 and that the (X,, Yg) are i.i.d. with each coordinate having a standard normal distribution, nd the probability that the insect is at 50 units above the y = a: line (relative to the origin at time 0). (ii) Consider the total distance that the y has actually ovvn starting from time 0. Under the assumptions of (i), nd an approximation to the probability that this quantity is between 75 and 150. (15)