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4. Sampling Without Replacement We have n−2 beer bottles b1,…,bn−2 and 2 cider bottles c1 and c2 ....

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Advance Math

4. Sampling Without Replacement

We have n−2 beer bottlesb1,…,bn−2 and 2 cider bottlesc1 and c2 . Consider a uniformly randompermutation π1,…,πn of these nbottles (so that each of the n! permutations is equallylikely).

  1. Let X be the index of the first beer bottle in thepermutation. That is,{π1,…,πX−1}⊆{c1,c2}and πX∈{b1,…,bn} .What is E[X] ?
  2. Let Y be the index of the first cider bottle in thepermutation. That is{π1,…,πY−1}⊆{b1,…,bn}and πX∈{c1,c2} . What isE[Y] ?

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