A 14-year-old patient presents with a mediastinal mass, a WBC of 110 × 109/L, hepatosplenomegaly, and early central nervous system involvement. Both L1 and L2 morphology are seen, and surface markers CD7, CD2, and CD5 are expressed. Which type of ALL is present?

Compute the average number of customers (waiting or being served) in S1. Show your work on the scratch paper. Compute two digits after the decimal point.

A more detailed data study reveals that the arrival rate of all types depends on the elapsed time in hours since the service desk opens taking the following form: 

Let X(t) be the number of jobs in the system. Define your state space (e.g., {A,B,C}) for X(t) below and draw the rate diagram for X(t) on your scratch paper. 

How was the public image of women during the 1950’s different from the WWII image of Rosie the Riveter? 

Given that in the first 30 minutes, 5 customers arrive, what is the probability that 3 of them are type A (and 2 are type B)? Provide four digits after the decimal point. Show your work on the scratch paper.

Someone claims that the stationary probabilities for the DTMC is

What is the distribution of the number of Type A customers arriving in a 2-hour period? Specify the distribution and its mean. Distribution: [dist] Mean: [mean]

Customers arrive at a service desk according to a Poisson process with rate

A server system consists of two identical servers. Jobs arrive according to a Poisson process with rate 4 per hour, and each job is served by one server. Service times are exponentially distributed with rate 3 per hour per server. That is, if both servers are busy, the total service rate is 6 per hour. The system can hold a maximum of 3 jobs (including jobs in service and in the queue). Any arriving job when the system already has 3 jobs is rejected (lost). Show your work on your scratch paper answering Q4-Q7.