benchmarks.wiki

benchmarks.wiki / Public workspace

MMLU-Pro / 8849 / Let W(t) be a Bownian motion, Let E[exp(i*W(t))]:= E[cos(W(t))+i*sin(W(t))],…

Problem

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

question

Let W(t)W(t) be a Bownian motion, Let $E[exp(i*W(t))]:= E[cos(W(t))+i*sin(W(t))]$, where i=−1i=\sqrt{-1}. Is $M(t):=exp(i*W(t))/E[exp(i*W(t))]$ a matingale? Return 1 for yes and 0 for no.
Plain-text mathematical notation (without MathML)
Let W(t) be a Bownian motion, Let $E[exp(i*W(t))]:= E[cos(W(t))+i*sin(W(t))]$, where i=√(−1). Is $M(t):=exp(i*W(t))/E[exp(i*W(t))]$ a matingale? Return 1 for yes and 0 for no.
Original LaTeX notation
Let $W(t)$ be a Bownian motion, Let $E[exp(i*W(t))]:= E[cos(W(t))+i*sin(W(t))]$, where $i=\sqrt{-1}$. Is $M(t):=exp(i*W(t))/E[exp(i*W(t))]$ a matingale? Return 1 for yes and 0 for no.

category

math

options

  1. i (the imaginary unit)
  2. 1.0
  3. -0.5
  4. 2.0
  5. 1.5
  6. 0.0
  7. -2.0
  8. 3.0
  9. 0.5
  10. -1.0

src

theoremQA-Math

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

Source and history

upstream_id / Original problem ID
8849
task_id
d1a386d5-d929-5e32-b15e-da4b52281d28
task_key
default--test--8849
task_revision_id
1
config / split
default / test

Official source

initial import