TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/12.7

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’Probability and Statistics’ exercises

A tutor of ’probability and statistics’ exercises claims that every student that is asked to present the solution for a problem on blackboard is randomly sampled (uniformly) with replacement among all students, for each problem. Every sheet contains of seven problems. After the sixth exercise session a motivated student mentions the following:

(a) ’Every student in class was asked to present exactly once.’ What is the probability for that? Do the data support the tutor’s statement?
(b) ’Two students were asked to present half of the exercises each.’ What is the probability for that, if the number of students is the same as in (a)?
(c) What is the probability for the observations in (a) and (b) if the students were sampled without replacement?

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