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MMLU-Pro / 8506 / Let N₁(t) and N₂(t) be two independent Posson processes with rate…

Problem

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

question

Let N1(t)N_1(t) and N2(t)N_2(t) be two independent Posson processes with rate λ1=1\lambda_1 = 1 and λ2=2\lambda_2 = 2, respectively. Let N(t) be the merged process N(t) = N_1(t) + N_2(t). Given that N(1) = 2, Find the probability that N_1(1) = 1.
Plain-text mathematical notation (without MathML)
Let N₁(t) and N₂(t) be two independent Posson processes with rate λ₁=1 and λ₂=2, respectively. Let N(t) be the merged process N(t) = N_1(t) + N_2(t). Given that N(1) = 2, Find the probability that N_1(1) = 1.
Original LaTeX notation
Let $N_1(t)$ and $N_2(t)$ be two independent Posson processes with rate $\lambda_1 = 1$ and $\lambda_2 = 2$, respectively. Let N(t) be the merged process N(t) = N_1(t) + N_2(t). Given that N(1) = 2, Find the probability that N_1(1) = 1.

category

math

options

  1. 0.3679
  2. 0.7368
  3. 0.3333
  4. 0.4444
  5. 0.5555
  6. 0.1494
  7. 0.1839
  8. 0.4060
  9. 0.2635
  10. 0.6666

src

theoremQA-Math

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Source and history

upstream_id / Original problem ID
8506
task_id
1d262bd9-f2ad-5b4a-9301-0d77ddbb589c
task_key
default--test--8506
task_revision_id
1
config / split
default / test

Official source

initial import