## Calculus (3rd Edition)

$\approx 0.982$
We are given that $p(x)=Ce^{-x} e^{-e^{-x}}$ Suppose that $a =-e^{-x} \implies da=e^{-x} dx$ Consider $I=\int_{-\infty}^{\infty} Ce^{-x} e^{-e^{-x}} dx \\=C \int_{-\infty}^{\infty} e^{u} du\\=C \lim\limits_{R \to \infty}(e^{-e^{-R}}-e^{-e^{R}}) \\=C(1-0)\\=C$ We will find $P(-4 \leq X \leq 4)=\int_{-4}^{4} p(x) \ dx\\=\int_{-4}^4 e^{-x} e^{-e^{-x}} \\=[e^{-e^{-x}}]_{-4}^4 \\=e^{-e^{-4}}-e^{-e^{4}} \approx 0.982$