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MMLU-Pro / 7992 / 5.3-1. Let X₁ and X₂ be independent Poisson random variables with…

Problem

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

question

5.3-1. Let X1X_1 and X2X_2 be independent Poisson random variables with respective means λ1=2\lambda_1=2 and λ2=3\lambda_2=3. Find (a) P(X1=3,X2=5)P\left(X_1=3, X_2=5\right). HINT. Note that this event can occur if and only if {X1=1,X2=0}\left\{X_1=1, X_2=0\right\} or {X1=0,X2=1}\left\{X_1=0, X_2=1\right\}.
Plain-text mathematical notation (without MathML)
5.3-1. Let X₁ and X₂ be independent Poisson random variables with respective means λ₁=2 and λ₂=3. Find
(a) P(X₁=3,X₂=5).
HINT. Note that this event can occur if and only if {X₁=1,X₂=0} or {X₁=0,X₂=1}.
Original LaTeX notation
5.3-1. Let $X_1$ and $X_2$ be independent Poisson random variables with respective means $\lambda_1=2$ and $\lambda_2=3$. Find
(a) $P\left(X_1=3, X_2=5\right)$.
HINT. Note that this event can occur if and only if $\left\{X_1=1, X_2=0\right\}$ or $\left\{X_1=0, X_2=1\right\}$.

category

math

options

  1. 0.0137
  2. 0.0084
  3. 0.0157
  4. 0.0168
  5. 0.0182
  6. 0.0245
  7. 0.0101
  8. 0.0213
  9. 0.0125
  10. 0.0226

src

scibench-stat

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Source and history

upstream_id / Original problem ID
7992
task_id
a8409548-2c21-510a-b5ff-c7de859bf8ee
task_key
default--test--7992
task_revision_id
1
config / split
default / test

Official source

initial import