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MMLU-Pro / 10697 / Let X be uniformly distributed over {1,2,…,m}. Assume m=2^(n) . We…

Problem

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question

Let XX be uniformly distributed over {1,2,…,m}\{1, 2, \ldots, m\}. Assume m=2nm=2^n . We ask random questions: Is X∈S1X\in S_1? Is X∈S2X\in S_2? ... until only one integer remains. All 2m2^m subsets of {1,2,…,m}\{1, 2, \ldots, m\} are equally likely. Suppose we ask n+nn+\sqrt{n} random questions. Use Markov's inequality to find the probability of error (one or more wrong objects remaining) when nn goes to infinity?
Plain-text mathematical notation (without MathML)
Let X be uniformly distributed over {1,2,…,m}. Assume m=2^(n) . We ask random questions: Is X∈S₁? Is X∈S₂? ... until only one integer remains. All 2^(m) subsets of {1,2,…,m} are equally likely. Suppose we ask n+√(n) random questions. Use Markov's inequality to find the probability of error (one or more wrong objects remaining) when n goes to infinity?
Original LaTeX notation
Let $X$ be uniformly distributed over $\{1, 2, \ldots, m\}$. Assume $m=2^n$ . We ask random questions: Is $X\in S_1$? Is $X\in S_2$? ... until only one integer remains. All $2^m$ subsets of $\{1, 2, \ldots, m\}$ are equally likely. Suppose we ask $n+\sqrt{n}$ random questions. Use Markov's inequality to find the probability of error (one or more wrong objects remaining) when $n$ goes to infinity?

category

computer science

options

  1. 0.3
  2. 0.4
  3. 0.1
  4. 0.0
  5. 0.7
  6. 0.2
  7. 0.5
  8. 1.0
  9. 0.8
  10. 0.6

src

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Source and history

upstream_id / Original problem ID
10697
task_id
a3141ebc-f174-52f4-b24e-4ec643273705
task_key
default--test--10697
task_revision_id
1
config / split
default / test

Official source

initial import