Define univariate, bivariate, and multivariate data analysis. Review box 15.2 and give 2 examples of evaluation questions for each type of data analysis in regards to an STD program for college students.

I need help with creating 2 sample evaluation questions for multivariate analysis.

multivariate analysis - the examination of more than two variables simultaneously (e.g., the relationship between gender, race, and college graduation)

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 t. Then, the process (Xt : 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 7 [15 points = 5 + 10] Consider a queuing system M/M/co with unlimited number of servers that is functioning under stationary distribution. Customer arrivals form a Poisson process that has rate A = 30 per hour. Service times are independent exponentially distributed with average = = 15 minutes. Focus on the departure process, {D(t) : t 2 0} assuming that the system is operating under stationary distribution. Consider a random variable, 7, which is independent of D = { D(t) : # 2 0} and its density function is: f (t) = 25t . exp(-5t) for t > 0. where { is measured in hours. Set Y = D(T). 1. Derive expectation of Y. 2. Evaluate variance of Y.Show that if the detailed balance equations for the B&D process are satisfied, then the limiting distribution equations (6.35) are satisfied. Show that this is true in general, that is if there is the solution to the detailed balance equations, then the stationary equations 0 = > Wk qkj - "j lj, j = 0, 1, 2, .. . are satisfied. (c) An example where we have a stationary solution, but the detailed balance equations have no solution, is given by the infinitesimal matrix 3 A = 2 Find the stationary distribution for this chain and show that the detailed balance equa- tions have no solution. Can you give verbal description of how this chain moves in the long run? How is this compared to the interpretation at the end of question (a)?4.14. Consider the model of Conceptual Problem 4.2. Suppose the arrival rate is 20 customers per hour and the average service time is 4 minutes. Compute the expected amount of time three tellers are working during an 8-hour day, assuming there are no customers in the bank at the beginning of the day