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MMLU-Pro / 8625 / Let X_n: n …

Problem

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question

Let {X_n: n \geq 1} be independent, identically distributed random variables taking integer values {1,-1}. Let S_0=0, S_n=\sum_{i=1}^n X_i. Let P(X_i=1)=0.8 and P(X_i=-1)=0.2. The range R_n of S_0,S_1,...,S_n is the number of distinct values taken by the sequence. Then what is the limit of n^{-1}E[R_n] as n goes to infinity? Here E[R_n] is the expectation over the random variable R_n.

category

math

options

  1. 1.0
  2. 0.5
  3. 1.2
  4. 1.6
  5. 0.8
  6. 0.9
  7. 1.4
  8. 0.2
  9. 0.6
  10. 0.4

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8625
task_id
9f218b08-f925-5ad7-8b16-1a6d5e1025ad
task_key
default--test--8625
task_revision_id
1
config / split
default / test

Official source

initial import