1)
P(xy<1)很简单,就是对下图阴影的面积求二重积分
∫(1/2~2)∫(1/2~1/y) 1/(4x²y³) dxdy
= ∫(1/2~2) 1/(4(1/2)y³)-1/(4(1/y)y³) dy
=∫(1/2~2) 1/(2y³)-1/(4y²) dy
=(-1/(4y²)+1/(4y))|(1/2~2)
=(-1/16+1/8)-(-1+1/2)
=1/16+1/2
=9/16
3)
∫(1~3)∫(1/2~) 1/(4x²y³) dydx
= ∫(1~3) {1/(8x²(1/4))}dx
=-1/(2x) |(1~3)
=1/2-1/6
=1/3