What is the difference between A/B testing and Multivariate testing?Describe a situation where an A/B test would be more suited as a data-gathering method than a multivariate testWhat is the difference between A/B testing and Multivariate testing?Describe a situation where an A/B test would be more suited as a data-gathering method than a multivariate test

3. (a) During lunch hour, arrivals of customers at a pizza hut restaurant follows a Poisson process with the rate of 120 customers per hour. The restaurant has one line, with three workers taking food orders at independent services stations. Each worker takes an exponen- tially distributed amount of time-on average 1 minute-to serve a customer. Let X, denote the number of customers in the restaurant (in line and being serviced) at time f. Then, the process (X, : 1 2 0) is a continuous-time Markov chain. (i) Show that the process is a birth-and-death process by giving the birth and death rates. [4 marks] (ii) Find the generator matrix of the above process. [5 marks ] (iii) For each integer & 2 0, derive the long-term probability that there are & customers in the restaurant. [8 marks ] (iv) Calculate the long-term probability that all three workers are busy. [6 marks ] (v) Find the average number of customers in the restaurant in the long term. [7 marks ] (b) A student support center has 3 tutors who help students with their home work. Students arrive at the center according to a Poisson process at rate A = 3 per hour. Each tutor's service time is exponentially distributed with average of 1/10 hours. Tutors' service times and student arrival times are independent. If all the tutors are busy when a student arrives at the center, the student will leave. Let X, denote the number of tutors who are busy at time t. Determine its generator matrix and stationary distribution. [10 marks ]Problem 2: 10 points Consider a birth-and-death process, X = {X(t) : t 2 0} , associated with the service line that consists of N = 10 servers. When all 10 servers are occupied, the new request is refused and not coming into the service line. As there are k k =3. (10 -k) for 0 10, and P [X(t + 4) - X(t) = -1\\X(t) = k] =/k = 2 . k for 0