IND ENG 173Practice Second MidtermIntroduction to Stochastic ProcessesApril 3, 2018Prof. Mariana Olvera-CraviotoPage 1 of 7Practice Second Midterm ExamPlace all answers on the question sheet provided. The exam is closed textbook/notes/handouts/homework.You are allowed to bring a 2-page cheat sheet and a calculator, but not a computer or a smartphone.Write all answers clearly and in complete sentences. All answers should be supported by analysis or anargument. This exam has a total of 60 points, and is meant to be completed in 1.25 hour1. Incoming calls into an airline’s call center come from two types of customers: regular cus-tomers and high priority customers (those with high frequent flyer status). Each arriving callwill be from a regular customer with probability 0.8, independently of all other calls. Thetotal number of calls is modeled as a Poisson process{N(t) :t≥0}with rate 10 per minute.LetNp(t) denote the number of calls from priority customers during the period [0, t].(a)[5 pts]Compute the probability that there were 5 calls from priority customers between6:00 pm and 6:10 pm.

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(b)[6 pts]Write down the PMF ofNp(t) givenN(t) =n.

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