Now you try one that has a little different twist to it. Reverse the order of integration in the integral
\(\int_{0}^1 \int_x^{2x} f(x,y)\ dy \ dx.\)
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Because of the nature of this region, when we reverse the order of integration, we need two integrals.
\(\int_{0}^1 \int_x^{2x} f(x,y)\ dy \ dx = \int_{0}^1 \int_{y/2}^{y} f(x,y)\ dx \ dy + \int_{1}^2 \int_{y/2}^{1} f(x,y)\ dx \ dy\)
The next step is to apply this knowledge to probability. Your text will explain how to do that. Good luck on your actuarial exam! Click here to go back to the beginning and start over.