During the party the Dean suddenly wants to know who won most Christmas cookies in the...

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During the party the Dean suddenly wants to know who won most Christmas cookies in the "Bing or Ding" game. He suggests the following algorithm: Algorithm 1: Find student with most cookies max -∞ s+null Randomly order the students. Let $₁,..., 8, be the students in this random order. Let c, denote the number of cookies won by student s. for i = 1,...,n do if if c> max then | max ←c and ss; (*) end end return s In the following assume that all students won a different amount of cookies. That is, c₁ c, for all i j. Question 7.1 What is the probability that the line (*) is executed at the last iteration? Question 7.2 Let X, be a random variable that is 1 if line (*) is executed in iteration i and 0 otherwise. What is probability that X = During the party the Dean suddenly wants to know who won most Christmas cookies in the "Bing or Ding" game. He suggests the following algorithm: Algorithm 1: Find student with most cookies max -∞ s+null Randomly order the students. Let $₁,..., 8, be the students in this random order. Let c, denote the number of cookies won by student s. for i = 1,...,n do if if c> max then | max ←c and ss; (*) end end return s In the following assume that all students won a different amount of cookies. That is, c₁ c, for all i j. Question 7.1 What is the probability that the line (*) is executed at the last iteration? Question 7.2 Let X, be a random variable that is 1 if line (*) is executed in iteration i and 0 otherwise. What is probability that X =

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