Question

There are 8 students in the class. At the beginning of each class. the professor draws...

There are 8 students in the class. At the beginning of each class. the professor draws a card to determine who will present the homework on the board. Suppose there is one question each day and each card draw is independent of all the others.

a) What is the expected waiting time from the beginning of the semester until everyone will have presented at least one problem?

b) After few weeks, there are two people who have still not presented. What is the expected waiting time from now until everyone has presented at least once?

Math   Statistics-And-Probability   
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Answer #1

This is coupon collector problem

a)

the expected number of attempts needed to get all n values is

b)

the random time until any of two people appears who have still not presented is geometrically distributed with parameter of success   p = 2/8 hence mean = 1/p = 4

then the expected time to get last people to present first time = 1/(1/8) = 8

hence

the expected waiting time from now until everyone has presented at least once = 8 + 4 = 12

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