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

4. Sampling Without Replacement

We have n−2 beer bottles b1,…,bn−2 and 2 cider bottles c1 and c2 . Consider a uniformly random permutation π1,…,πn of these n bottles (so that each of the n! permutations is equally likely).

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

Expert Solution

Colby Messinger answered 2 years ago

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