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Romeo and Juliet plan to meet each other at the Theta Pond on the Va.pdf

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Romeo and Juliet plan to meet each other at the Theta Pond on the Valentine’s Day. Assume that they arrive independently at random times between 5:00 pm and 6:00 pm (uniform distribution), and due to the cold weather, they agree not to wait more than 20 minutes for the other. (a) Find the probability that they will meet. (b) If Romeo arrives first, and Juliet arrives within 20 minutes (they meet each other!), find Romeo’s expected waiting time under these conditions. (c) Forget the conditions in (b), find Romeo’s overall expected waiting time. Solution a)probality = 20/60 =1/3 b) expected waiting =20 minute c) oveall waitin = 60-20 =40.

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Romeo and Juliet plan to meet each other at the Theta Pond on the Valentine’s Day. Assume that they arrive independently at random times between 5:00 pm and 6:00 pm (uniform distribution), and due to the cold weather, they agree not to wait more than 20 minutes for the other. (a) Find the probability that they will meet. (b) If Romeo arrives first, and Juliet arrives within 20 minutes (they meet each other!), find Romeo’s expected waiting time under these conditions. (c) Forget the conditions in (b), find Romeo’s overall expected waiting time. Solution a)probality = 20/60 =1/3 b) expected waiting =20 minute c) oveall waitin = 60-20 =40

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  • 1. Romeo and Juliet plan to meet each other at the Theta Pond on the Valentine’s Day. Assume that they arrive independently at random times between 5:00 pm and 6:00 pm (uniform distribution), and due to the cold weather, they agree not to wait more than 20 minutes for the other. (a) Find the probability that they will meet. (b) If Romeo arrives first, and Juliet arrives within 20 minutes (they meet each other!), find Romeo’s expected waiting time under these conditions. (c) Forget the conditions in (b), find Romeo’s overall expected waiting time. Solution a)probality = 20/60 =1/3 b) expected waiting =20 minute c) oveall waitin = 60-20 =40