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MMLU-Pro / 8855 / Let N(t), t …λ=4…

Problem

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

question

Let {N(t), t \in [0, \infty)} be a Poisson process with rate of λ=4\lambda = 4 and X1X_1 be the first arrival time. Given N(t) = 1, then what is P(X1<=t/2)P(X_1 <= t / 2)?
Plain-text mathematical notation (without MathML)
Let {N(t), t \in [0, \infty)} be a Poisson process with rate of λ=4 and X₁ be the first arrival time. Given N(t) = 1, then what is P(X₁<=t/2)?
Original LaTeX notation
Let {N(t), t \in [0, \infty)} be a Poisson process with rate of $\lambda = 4$ and $X_1$ be the first arrival time. Given N(t) = 1, then what is $P(X_1 <= t / 2)$?

category

math

options

  1. 0.5
  2. 1
  3. 0.95
  4. 0.65
  5. 0.85
  6. 0.15
  7. 0.75
  8. 0.25
  9. 0.4
  10. 0.3

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8855
task_id
eb4c4d3f-8399-5c9d-af95-4c09c4ed33cf
task_key
default--test--8855
task_revision_id
1
config / split
default / test

Official source

initial import