Orders arrive at a Web site according to a Poisson process with a mean of 12 per hour. Determine the following: (a) Probability of no orders in five minutes. (b) Probability of 3 or more orders in five minutes. (c) Probability of no orders arrive until after ten minutes. (d) Length of a time interval such that the probability of no orders in an interval of this length is 0.001. (e) Use R to calculate the probabilities in parts (a) and (b). Show the R codes and outputs in R. P111 4-6 (modified) (18 pt) Suppose that the probability density function of a random variable X is ( 4)( ) , 4 xfxxe = > . (a) Find the following probabilities: a1. P(X>1) a2. P(25) a4. Find x such that P(X