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MMLU-Pro / 7997 / 7.5-1. Let Y₁<Y₂<Y₃<Y₄<Y₅<Y₆ be the order statistics of a…

Problem

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

question

7.5-1. Let Y1<Y2<Y3<Y4<Y5<Y6Y_1 < Y_2 < Y_3 < Y_4 < Y_5 < Y_6 be the order statistics of a random sample of size n=6n=6 from a distribution of the continuous type having (100p)(100 p) th percentile πp\pi_p. Compute (a) P(Y2<π0.5<Y5)P\left(Y_2 < \pi_{0.5} < Y_5\right).
Plain-text mathematical notation (without MathML)
7.5-1. Let Y₁<Y₂<Y₃<Y₄<Y₅<Y₆ be the order statistics of a random sample of size n=6 from a distribution of the continuous type having (100p) th percentile π_(p). Compute
(a) P(Y₂<π_(0.5)<Y₅).
Original LaTeX notation
7.5-1. Let $Y_1 < Y_2 < Y_3 < Y_4 < Y_5 < Y_6$ be the order statistics of a random sample of size $n=6$ from a distribution of the continuous type having $(100 p)$ th percentile $\pi_p$. Compute
(a) $P\left(Y_2 < \pi_{0.5} < Y_5\right)$.

category

math

options

  1. 0.7137
  2. 0.8426
  3. 0.6561
  4. 0.8750
  5. 0.9000
  6. 0.5000
  7. 0.6214
  8. 0.3125
  9. 0.9453
  10. $0.7812$

src

scibench-stat

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Source and history

upstream_id / Original problem ID
7997
task_id
74971056-410d-5cab-965b-46bb499eacb7
task_key
default--test--7997
task_revision_id
1
config / split
default / test

Official source

initial import