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MMLU-Pro / 8215 / Let X_1, X_2,... be independent variables each taking values +1 or -1 with…

Problem

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

question

Let X_1, X_2,... be independent variables each taking values +1 or -1 with probabilities 1/2 and 1/2. It is know that $\sqrt{3/n^3}*\sum_{k=1}^n k*X_k$ converges in distribution normal distribution N(a,b) as n goes to infinity. Here a is the expectation and b is the variance. What are the values of a and b? Return the answers as a list. For example, if a=2, b=100, return [2,100].
Plain-text mathematical notation (without MathML)
Let X_1, X_2,... be independent variables each taking values +1 or -1 with probabilities 1/2 and 1/2. It is know that $\sqrt{3/n^3}*\sum_{k=1}^n k*X_k$ converges in distribution normal distribution N(a,b) as n goes to infinity. Here a is the expectation and b is the variance. What are the values of a and b? Return the answers as a list. For example, if a=2, b=100, return [2,100].
Original LaTeX notation
Let X_1, X_2,... be independent variables each taking values +1 or -1 with probabilities 1/2 and 1/2. It is know that $\sqrt{3/n^3}*\sum_{k=1}^n k*X_k$ converges in distribution normal distribution N(a,b) as n goes to infinity. Here a is the expectation and b is the variance. What are the values of a and b? Return the answers as a list. For example, if a=2, b=100, return [2,100].

category

math

options

  1. [2, 0]
  2. [0, 1]
  3. [2, 1]
  4. [1, 1]
  5. [1, 0]
  6. [0, 0]
  7. [0, 1/2]
  8. [1, 2]
  9. [0, 2]
  10. [0, 3]

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8215
task_id
15c2c1c9-d650-57d5-aad1-618154342fd5
task_key
default--test--8215
task_revision_id
1
config / split
default / test

Official source

initial import