per day. At the end of each day, they do the following: for each of the candidates active durin day, randomly with probability 0.5 and indepdently, determine if the candidate is permanentl he show or will participate at least for the next day. They start, on day 1, with n participan stop when only one participant remains. Please help the TV company to answer the following questions without providing a proof, jus e answers: • What is the expected number of days a participant appears? • How many participants can we expect to be on the second of the show? How many participants can we expect to be on the ith day? For how many days can we expect the TV show to run? What is the expected total number of songs that will be heard in total?

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Chapter1: Combinatorial Analysis
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Scenario: A TV company has a game show running over several days. Each participant sings one
song per day. At the end of each day, they do the following: for each of the candidates active during
the day, randomly with probability 0.5 and indepdently, determine if the candidate is permanently
off the show or will participate at least for the next day. They start, on day 1, with n participants
and stop when only one participant remains.
Please help the TV company to answer the following questions without providing a proof, just
state answers:
• What is the expected number of days a participant appears?
• How many participants can we expect to be on the second of the show?
• How many participants can we expect to be on the ith day?
• For how many days can we expect the TV show to run?
• What is the expected total number of songs that will be heard in total?
Transcribed Image Text:Scenario: A TV company has a game show running over several days. Each participant sings one song per day. At the end of each day, they do the following: for each of the candidates active during the day, randomly with probability 0.5 and indepdently, determine if the candidate is permanently off the show or will participate at least for the next day. They start, on day 1, with n participants and stop when only one participant remains. Please help the TV company to answer the following questions without providing a proof, just state answers: • What is the expected number of days a participant appears? • How many participants can we expect to be on the second of the show? • How many participants can we expect to be on the ith day? • For how many days can we expect the TV show to run? • What is the expected total number of songs that will be heard in total?
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