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MMLU-Pro / 8939 / Let G_n(s) be the probability generating function of the size Z_n of the n-th…

Problem

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

question

Let G_n(s) be the probability generating function of the size Z_n of the n-th generation of a branching process, where Z_0=1 and var(Z_1)>0. Let H_n be the inverse function of the function G_n, viewed as a function on the interval [0, 1].  Is M_n= {H_n(s)}^{Z_n} defines a martingale with respect to the sequence Z? Return 1 for yes and 0 for no.

category

math

options

  1. 1.0
  2. 1.5
  3. 0.5
  4. 3.0
  5. 4.0
  6. -1.0
  7. 0.0
  8. -0.5
  9. -2.0
  10. 2.0

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8939
task_id
e7b51565-4f81-5c98-a293-d13f01cc2be4
task_key
default--test--8939
task_revision_id
1
config / split
default / test

Official source

initial import