Integration with Probability.

• Mar 7th 2011, 10:16 PM
galeontiger
Integration with Probability.
Hello, I was wondering if anyone would be able to explain how the solution got from the E(Profit) = integral line to the next line.
A full step by step of the entire question would be preferred.
Thank you so much for your time.
-GaleonTiger

Attachment 21079
• Mar 9th 2011, 10:33 AM
Focus
Lump the integral terms together using $\int_{-\infty}^x g+\int^{\infty}_x g =\int_{-\infty}^\infty g$.

Then use the fact that $\mathbb{P}(X \geq x)=\int_{x}^\infty f_X(u) du$ where f_X is the pdf of X.