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Omni-MATH / Yannick picks a number N randomly from the set of positive integers such that the probability that n is selected is 2^(−n) for each positive integer n. He then puts N identical sli…

Problem

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problem

Yannick picks a number NN randomly from the set of positive integers such that the probability that nn is selected is 2−n2^{-n} for each positive integer nn. He then puts NN identical slips of paper numbered 1 through NN into a hat and gives the hat to Annie. Annie does not know the value of NN, but she draws one of the slips uniformly at random and discovers that it is the number 2. What is the expected value of NN given Annie's information?
Plain-text mathematical notation (without MathML)
Yannick picks a number N randomly from the set of positive integers such that the probability that n is selected is 2^(−n) for each positive integer n. He then puts N identical slips of paper numbered 1 through N into a hat and gives the hat to Annie. Annie does not know the value of N, but she draws one of the slips uniformly at random and discovers that it is the number 2. What is the expected value of N given Annie's information?
Original LaTeX notation
Yannick picks a number $N$ randomly from the set of positive integers such that the probability that $n$ is selected is $2^{-n}$ for each positive integer $n$. He then puts $N$ identical slips of paper numbered 1 through $N$ into a hat and gives the hat to Annie. Annie does not know the value of $N$, but she draws one of the slips uniformly at random and discovers that it is the number 2. What is the expected value of $N$ given Annie's information?

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Source and history

task_id
d3de04a5-578a-5446-a1f7-3f1af46a4cab
task_key
test--d3de04a5-578a-5446-a1f7-3f1af46a4cab
task_revision_id
1
config / split
/ test

Official source

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