X=reaction time, Y=length of life of electronic components Continuous joint probability distribution:
Compute: P(0 < X < 0.6 and 0.25 < Y < 0.5)
"f(x,y)=\\left\\{\\begin{matrix}\n\n4xy, 0<x<1.0, 0<y<1 & \\\\\n\n0, elsewhere &\n\n\\end{matrix}\\right."
"P= \\int \\int F(x,y) dx dy"
P(0<x<0.5 + 0.25<y<0.5) fall in this region.
"P = \\int^{0.6}_0 \\int^{0.5}_{0.25} 4 xy dydx \\\\\n\nP = \\int^{0.6}_0 [4x (\\frac{y^2}{2})]^{0.5}_{0.25} dx \\\\\n\n= \\int^{0.6}_0 2x [(\\frac{1}{2})^2 -(\\frac{1}{4})^2]dx \\\\\n\n= (\\frac{3}{8})\\int^{0.6}_0 xdx \\\\\n\n= \\frac{3}{8}(\\frac{x^2}{2})^{0.6}_0 \\\\\n\n= \\frac{3}{8}(0.6)^2 \\\\\n\n= 0.0675"
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