answer all questions with explanation

Consider the capacitated queueing model discussed in class, and assume that K =6. i.e., at most 6 people can be in the system at the same time. Suppose we start with an empty system (i.e., X. = 0). Assuming that the number of people arriving during each period has binomial distribution with parameters N = 4, p = 0.2, compute: (a) The probability of the sample path (0, 1, 3, 4, 3, 2). (b) P(X, = j). j =1,2,3, 4,5,6. (c) P(X, = 4, X, = 1) . (d) P(X, = 4|X2 = 1)