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MMLU-Pro / 9038 / 5.3-7. The distributions of incomes in two cities follow the two Pareto-type…

Problem

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question

5.3-7. The distributions of incomes in two cities follow the two Pareto-type pdfs f(x)=2x3,1<x<∞, and g(y)=3y4,1<y<∞, f(x)=\frac{2}{x^3}, 1 < x < \infty , \text { and } g(y)= \frac{3}{y^4} , \quad 1 < y < \infty, respectively. Here one unit represents $20,000\$ 20,000. One person with income is selected at random from each city. Let XX and YY be their respective incomes. Compute P(X<Y)P(X < Y).
Plain-text mathematical notation (without MathML)
5.3-7. The distributions of incomes in two cities follow the two Pareto-type pdfs
f(x)=(2)/(x³),1<x<∞, and g(y)=(3)/(y⁴), 1<y<∞,
respectively. Here one unit represents $20,000. One person with income is selected at random from each city. Let X and Y be their respective incomes. Compute P(X<Y).
Original LaTeX notation
5.3-7. The distributions of incomes in two cities follow the two Pareto-type pdfs
$$
f(x)=\frac{2}{x^3}, 1 < x < \infty , \text { and } g(y)= \frac{3}{y^4} ,  \quad 1 < y < \infty,
$$
respectively. Here one unit represents $\$ 20,000$. One person with income is selected at random from each city. Let $X$ and $Y$ be their respective incomes. Compute $P(X < Y)$.

category

math

options

  1. $\frac{1}{2}$
  2. $\frac{3}{5}$
  3. $\frac{4}{5}$
  4. $\frac{3}{4}$
  5. $\frac{2}{3}$
  6. $\frac{1}{4}$
  7. $\frac{2}{5}$
  8. $\frac{1}{5}$
  9. $\frac{5}{6}$
  10. $\frac{1}{3}$

src

scibench-stat

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Source and history

upstream_id / Original problem ID
9038
task_id
39612cce-939f-5283-96f6-451cc65688fc
task_key
default--test--9038
task_revision_id
1
config / split
default / test

Official source

initial import