DISTRIBUTION THEORY Question 4 Assume that two customers, A and B, are due to arrive at a lawyer's office during the same hour from 10:00 to 11:00. Their actual arrival times, which we will denote by X and Y respectively, are independent of each other and uniformly distributed during the hour. (a) Find the probability that both customers arrive within the last fifteen minutes. (b) Find the probability that A arrives first and B arrives more than 30 minutes after A. (c) Find the probability that B arrives first provided that both arrive during the last half-hour. Question 7 Which of the following statements are true and which are false? Justify your answers! (a) Let the joint density function of two random variables X and Y be given by fx.y (x, y) , x20, y2 x. Then X and Y are independent if fx,r can be factorised as fx,r(x, y) = g(x)h(v) where g is a function of x only and h is a function of y only. (b) Assume that X" and Y are two continuous random variables. If fy (xly) = 0 for all values of x and y then X and Y are independent. (c) Assume that X and Y are two continuous random variables. If far (xly) = fx (y) for all values of y then X and Y are independent