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MMLU-Pro / 8326 / 5.3-3. Let X₁ and X₂ be independent random variables with probability…

Problem

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

question

5.3-3. Let X1X_1 and X2X_2 be independent random variables with probability density functions f1(x1)=2x1,0<x1<1f_1\left(x_1\right)=2 x_1, 0 < x_1 <1 , and f2(x2)=4x23f_2 \left(x_2\right) = 4x_2^3 , 0<x2<10 < x_2 < 1 , respectively. Compute (a) P(0.5<X1<1P \left(0.5 < X_1 < 1\right. and 0.4<X2<0.8)\left.0.4 < X_2 < 0.8\right).
Plain-text mathematical notation (without MathML)
5.3-3. Let X₁ and X₂ be independent random variables with probability density functions f₁(x₁)=2x₁,0<x₁<1, and f₂(x₂)=4x₂³ , 0<x₂<1, respectively. Compute
(a) P(0.5<X₁<1 and 0.4<X₂<0.8).
Original LaTeX notation
5.3-3. Let $X_1$ and $X_2$ be independent random variables with probability density functions $f_1\left(x_1\right)=2 x_1, 0 < x_1 <1 $, and $f_2 \left(x_2\right) = 4x_2^3$ , $0 < x_2 < 1 $, respectively. Compute
(a) $P \left(0.5 < X_1 < 1\right.$ and $\left.0.4 < X_2 < 0.8\right)$.

category

math

options

  1. $\frac{15}{125}$
  2. $\frac{36}{125}$
  3. $\frac{32}{125}$
  4. $\frac{24}{125}$
  5. $\frac{18}{125}$
  6. $\frac{45}{125}$
  7. $\frac{48}{125}$
  8. $\frac{30}{125}$
  9. $\frac{42}{125}$
  10. $\frac{40}{125}$

src

scibench-stat

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Source and history

upstream_id / Original problem ID
8326
task_id
97d86297-fc48-5f9d-a38d-f8c1d85b1118
task_key
default--test--8326
task_revision_id
1
config / split
default / test

Official source

initial import