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MMLU-Pro / 7978 / Let X₁,X₂,… be a sequence of independent indetically distributed…

Problem

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

question

Let X1,X2,…X_1, X_2, \ldots be a sequence of independent indetically distributed random variables drawn according to the probability mass function p(x)=N(0,1)p(x) = N(0,1). Let q(x)=N(1,1)q(x)=N(1,1) be another probability mass function. Use natural logarithm to evaluate lim−1nlogq(X1,X2,…,Xn)\lim -\frac{1}{n}\log{q(X_1,X_2,\ldots,X_n)} as n→∞n \to \infty.
Plain-text mathematical notation (without MathML)
Let X₁,X₂,… be a sequence of independent indetically distributed random variables drawn according to the probability mass function p(x)=N(0,1). Let q(x)=N(1,1) be another probability mass function. Use natural logarithm to evaluate lim−(1)/(n)logq(X₁,X₂,…,X_(n)) as n→∞.
Original LaTeX notation
Let $X_1, X_2, \ldots$ be a sequence of independent indetically distributed random variables drawn according to the probability mass function $p(x) = N(0,1)$. Let $q(x)=N(1,1)$ be another probability mass function. Use natural logarithm to evaluate $\lim -\frac{1}{n}\log{q(X_1,X_2,\ldots,X_n)}$ as $n \to \infty$.

category

math

options

  1. 2.1
  2. 1.4
  3. 0.5
  4. 3.5
  5. 2.8
  6. 1.8
  7. 0.7
  8. 3.1
  9. 2.5
  10. 1.1

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
7978
task_id
fe058748-2b10-55f8-b89c-4c26674204b7
task_key
default--test--7978
task_revision_id
1
config / split
default / test

Official source

initial import