Let P be a point chosen uniformly at random on a circle of constant radius R. where [111. Y1] represent the Euclidean coordinates of P. Note: A point is chosen uniformly at random on a circle of radius R. if its distance to the centre of the disk is xed and the angle to the s-axis is taken from a uniform distribution in the interval [(1.211] as illustrated in Fig. I11. Fig.1}. 1 a] Are the coordinates K1 and Y1, of P. correlated? Are the coordinates K1 and Y1. of P. independent? Justify your answer. [1' marks] b] Suppose that another point D = [112. Y2] is chosen uniformly at random from the same circle of radius R. Point {it is selected independently of point P. Let U denote the distance between points P and (2. Calculate EIUE]? [1|] merits] c] Assuming the R is a random variable uniformly distributed over the It}. 2n] range. What is the p-robabilityr that the circumference of the circle takes on a value between 1 and 2'? [B merits]