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MMLU-Pro / 10464 / Consider the discrete memoryless channel Y=XZ where X and Z are…

Problem

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

question

Consider the discrete memoryless channel Y=XZY=XZ where XX and ZZ are independent binary random variables that take on values 0 and 1. Let P(Z=1)=0.5P(Z=1)=0.5. Find the capacity of this channel in bits.
Plain-text mathematical notation (without MathML)
Consider the discrete memoryless channel Y=XZ where X and Z are independent binary random variables that take on values 0 and 1. Let P(Z=1)=0.5. Find the capacity of this channel in bits.
Original LaTeX notation
Consider the discrete memoryless channel $Y=XZ$ where $X$ and $Z$ are independent binary random variables that take on values 0 and 1. Let $P(Z=1)=0.5$. Find the capacity of this channel in bits.

category

computer science

options

  1. 1.322
  2. 0.500
  3. 0.700
  4. 0.100
  5. 0.750
  6. 1.000
  7. 0.585
  8. 0.322
  9. 0.250
  10. 0.811

src

theoremQA-EECS

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Source and history

upstream_id / Original problem ID
10464
task_id
16ef969b-bb5f-520f-b3d9-88424c04b37c
task_key
default--test--10464
task_revision_id
1
config / split
default / test

Official source

initial import