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MMLU-Pro / 10534 / Suppose that (X,Y,Z) are jointly Gaussian and that …

Problem

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

question

Suppose that (X,Y,Z)(X, Y, Z) are jointly Gaussian and that X→Y→ZX \rightarrow Y \rightarrow Z forms a Markov chain. Let XX and YY have correlation coefficient 0.1 and let YY and ZZ have correlation coefficient 0.9. Find I(X;Z)I(X;Z) in bits.
Plain-text mathematical notation (without MathML)
Suppose that (X,Y,Z) are jointly Gaussian and that X→Y→Z forms a Markov chain. Let X and Y have correlation coefficient 0.1 and let Y and Z have correlation coefficient 0.9. Find I(X;Z) in bits.
Original LaTeX notation
Suppose that $(X, Y, Z)$ are jointly Gaussian and that $X \rightarrow Y \rightarrow Z$ forms a Markov chain. Let $X$ and $Y$ have correlation coefficient 0.1 and let $Y$ and $Z$ have correlation coefficient 0.9. Find $I(X;Z)$ in bits.

category

computer science

options

  1. 0.45
  2. 1.2
  3. 0.1
  4. 0.9
  5. 0.00587
  6. 0.15
  7. 0.6
  8. 0.7
  9. 0.025
  10. 0.3

src

theoremQA-EECS

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Source and history

upstream_id / Original problem ID
10534
task_id
4955b419-7b37-504d-af8a-35ab61243046
task_key
default--test--10534
task_revision_id
1
config / split
default / test

Official source

initial import