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MMLU-Pro / 8647 / 5.3-9. Let X₁,X₂ be a random sample of size n=2 from a distribution with…

Problem

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question

5.3-9. Let X1,X2X_1, X_2 be a random sample of size n=2n=2 from a distribution with pdf f(x)=3x2,0<x<1f(x)=3 x^2, 0 < x < 1. Determine (a) P(maxXi<3/4)=P(X1<3/4,X2<3/4)P\left(\max X_i < 3 / 4\right)=P\left(X_1<3 / 4, X_2<3 / 4\right)
Plain-text mathematical notation (without MathML)
5.3-9. Let X₁,X₂ be a random sample of size n=2 from a distribution with pdf f(x)=3x²,0<x<1. Determine
(a) P(maxX_(i)<3/4)=P(X₁<3/4,X₂<3/4)
Original LaTeX notation
5.3-9. Let $X_1, X_2$ be a random sample of size $n=2$ from a distribution with pdf $f(x)=3 x^2, 0 < x < 1$. Determine
(a) $P\left(\max X_i < 3 / 4\right)=P\left(X_1<3 / 4, X_2<3 / 4\right)$

category

math

options

  1. $\frac{625}{4096}$
  2. $\frac{512}{4096}$
  3. $\frac{841}{4096}$
  4. $\frac{343}{4096}$
  5. $\frac{729}{4096}$
  6. $\frac{800}{4096}$
  7. $\frac{961}{4096}$
  8. $\frac{567}{4096}$
  9. $\frac{676}{4096}$
  10. $\frac{900}{4096}$

src

scibench-stat

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Source and history

upstream_id / Original problem ID
8647
task_id
f3da6497-f609-588c-87cc-98fc47c05d58
task_key
default--test--8647
task_revision_id
1
config / split
default / test

Official source

initial import