A probability as an integral

Topic: Joint distributions · more questions on this topic
‹ A joint table Distribution function of a maximum ›

Explain how to calculate

\mathbb{P}\Bigl(\frac{X_1^2+\sin X_2}{X_1^2 X_2}>1\Bigr)

from the joint density of (X_1,X_2). Assume the expression under the probability is defined.

Worked answer (click to show)

Integrate the joint density over the region where (x_1^2+\sin x_2)/(x_1^2 x_2)>1.