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MMLU-Pro / 8502 / Suppose X_(n):n≥1 be independent and exponentially distributed with…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Suppose Xn:n≥1{X_n:n\geq 1} be independent and exponentially distributed with parameter 1. what is the probability $P(\limsup _{n \rightarrow infty} X_n/\log(n)=1)? Return a numeric value.
Plain-text mathematical notation (without MathML)
Suppose X_(n):n≥1 be independent and exponentially distributed with parameter 1. what is the probability $P(\limsup _{n \rightarrow infty} X_n/\log(n)=1)? Return a numeric value.
Original LaTeX notation
Suppose ${X_n:n\geq 1}$ be independent and exponentially distributed with parameter 1. what is the probability $P(\limsup _{n \rightarrow infty} X_n/\log(n)=1)? Return a numeric value.

category

math

options

  1. 0.5
  2. 1.0
  3. 0.1
  4. 0.36787944117 (1/e)
  5. 0.63212055882 (1 - 1/e)
  6. 0.845350936 (1 - 1/π)
  7. 0.0
  8. 0.69314718056 (1/ln(2))
  9. 0.9
  10. 0.2

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8502
task_id
653b2710-bd2c-56b3-9f2a-93487acba4cc
task_key
default--test--8502
task_revision_id
1
config / split
default / test

Official source

initial import