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?

Which specific cold agglutinin is present in 20% of patients with infectious mononucleosis?

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.

Let X and Y be two discrete random variables with the joint probability mass function (pmf) given by the table below: Y=0 Y=1 Y=2 X=0 0.1 0.1 0.1 X=1 0.1 0.2 0.1 X=2 0.05 0.05 0.2 Show your work on your scratch paper answering Q17-19.

What is the probability that the first two jobs are Type A? Show your work on the scratch paper.

Are X and Y independent? Choose your answer below and state the reason on the scratch paper.

Find the marginal distribution of X: P(X=0) = P(X=1) = P(X=2) =  

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 service station consists of two back-to-back stations S1 and S2. Customers follow this workflow: Customers first arrive at S1​, are served, and then proceed to S2​. After service at S2​, with probability 0.1, a customer is sent back to S1​ for rework (reentrant flow). Otherwise, with probability 0.9, the customer leaves the system. Assume the following conditions: The arrival process follows a Poisson distribution with rate 10 per hour. The service times at S1 and S2​ follow exponential distributions with means 5 minutes and 6 minutes​, respectively. S1 has a single server and S2 has two servers. Both have infinite queue capacity.

Consider a drive-through restaurant where all orders are processed by one order kiosk with virtually unlimited space for the cars to line up. Suppose one car arrive every 3 minutes, while it takes 90 seconds on average to take the order. Show your work on the scratch paper when answering Q20-Q22.