DREW \"11le i 1.7. Suppose that customers arrive at a facility according to a Poisson process having rate A = 2. Let X(t) be the number of customers that have arrived up to time t. Determine the following probabilities and conditional probabilities: (a) Pr{X(1) = 2}. (b) Pr[X(l) = 2 and X(3) = 6}. (c) Pr{X(l) = 2 X(3) = 6}. (d) Pr{X(3) = 6X(l) = 2}. 1.8. Let [X(t); t a 0} be a Poisson process having rate parameter A = 2. Determine the numerical values to two decimal places for the following probabilities: (a) Pr{X(1) s 2}. (b) mm) = land X(2) = 3}. (c) Pr{X(l) 2 2|X(l) a 1}