Answer should be typed format only without insert table and image.copied content strictly prohibited.

Consider an insect that starts flying from the origin at time 0. At time 1, it flies to the random point (X1, Y1). Starting from this point as the origin, it flies to a random point (X2, Y2), and so on. (i) Consider the co-ordinates of the fly at time 11 relative to its position at time 0. Assume that n = 100 and that the (Xi, Yi) are i.i.d. with each co-ordinate having a standard normal distribution, find the probability that the insect is at least 50 units above the y = 3:: line (relative to the origin at time 0). (ii) Consider the total distance that the fly has flown starting from time 0. Under the assumptions of (i), find an approximation to the probability that this quantity is between 75 and 150