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MMLU-Pro / 10463 / Suppose that feedback is used on a binary symmetric channel with parameter…

Problem

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question

Suppose that feedback is used on a binary symmetric channel with parameter p=0.5p=0.5. Each time a YY is received, it becomes the next transmission. Thus X1X_1 is Bern(1/2), X2=Y1X_2=Y_1, X3=Y2X_3=Y_2, \ldots, X_n=Y_{n-1}. Find limn→∞1nI(Xn;Yn)\lim_{n\to\infty} \frac{1}{n} I(X_n;Y_n) in bits.
Plain-text mathematical notation (without MathML)
Suppose that feedback is used on a binary symmetric channel with parameter p=0.5. Each time a Y is received, it becomes the next transmission. Thus X₁ is Bern(1/2), X₂=Y₁, X₃=Y₂, \ldots, X_n=Y_{n-1}. Find lim_(n→∞)(1)/(n)I(X_(n);Y_(n)) in bits.
Original LaTeX notation
Suppose that feedback is used on a binary symmetric channel with parameter $p=0.5$. Each time a $Y$ is received, it becomes the next transmission. Thus $X_1$ is Bern(1/2), $X_2=Y_1$, $X_3=Y_2$, \ldots, X_n=Y_{n-1}. Find $\lim_{n\to\infty} \frac{1}{n} I(X_n;Y_n)$ in bits.

category

computer science

options

  1. 1.25
  2. 1.0
  3. 2.0
  4. 1.5
  5. 0.5
  6. 0.75
  7. 0.9
  8. 0.0
  9. 0.25
  10. 0.1

src

theoremQA-EECS

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Source and history

upstream_id / Original problem ID
10463
task_id
a1713c27-d15e-5b04-917f-79948f8e7824
task_key
default--test--10463
task_revision_id
1
config / split
default / test

Official source

initial import