Word File Edit View Insert Format Tools Table Window Help HW 8 [Compatibility Mo

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Word File Edit View Insert Format Tools Table Window Help HW 8 [Compatibility Mode] Q Search in Document Home Insert Design Layout References Mailings Review View Share ^ Ee AaBbCcDdEe AaBbCcDc AaBbCcDdEe B l U.abe X2 X2 A, p...AE) Paste No SpaingHeading1 1HeadingTitle Styles Pane 1) Suppose passengers arrive to the immigration area of the airport according to a Poisson Process with rate -2min. Upon arrival, they split into two groups, US citizens and foreign nationals. On average, 60% of travelers are US citizens and 40% are foreign nationals. Answer the following questions for this system. (a) What is the probability that 40 US Citizens and 30 foreign nationals arrive in the first half an hour? (You can leave your answer as an expression) (b) Given that 2 foreign nationals arrived during the first 5 minutes, what kind of distribution does the arrival time of the first US Citizen have? What is the expected value of this arrival time? c) Given that 5 passengers arrived in the first 5 minutes, what is the probability that 3 were foreign nationals? Page 1 of1 139 words English (US) Focus + 150%

Explanation / Answer

Here = 2/ min

(a) So for half an hour expected number of passengers arriving at airport = 2/min * 30 = 60

so US citizen travelers = 60 * 60% = 36

Foreign Travelers = 60 * 40% = 24

Pr(40 US citizens ) = POISSON (40; 36)

Pr(30 Foreign citizens) = POISSON (30,24)

so Pr(40 citizens and 30 foreign citizens) = POISSON (40; 36) * POISSON (30, 24)

= e-36 3640 /40! *  e-24 2430 /30!

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