Question

1. The A vengers have just finished saving New York. They have decided to meet up at their new favorite shawarma place. The restaurant knows that Avengers will arrive according to a Poisson Process with an average interarrival time of 5 mirn (a) What is probability that exactly 6 of the avengers have entered the store after (b) What is the probability that fewer than 3 have arrived after 45 minutes? an hour. (c) Captain America and Iron Man are the next two Avengers who walk in. What is the probability they walk in within 1 minute of each other? The shawarma place knows that normal customers arrive to the shop according to Poisson Process with rate 6 per hour. These arrivals are independent of the Avengers arrivals. (d) What is the time until the first person walks in (Avenger or regular customer)? (e) What is probability that after 30 minutes, 5 people have arrived to the store? The shop has noticed that when a regular customer comes in, there is a 90% chance that they will be distracted by the Avengers and forget to order a meal. The average meal costs 10S. The Avengers eat for free (it's the Avengers) (f) What is the probability that after 1 hour, 5 regular customers have arrived and none of them have ordered a meal? (g) What is the expected revenue from meals after 4 hours?

Answer 1

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