Solution
= Solution
{c}
Normalization of the <probability density function> requires
$$
1=k\int_{-\pi/2}^{\pi/2}\cos^2x\,dx=k\frac\pi2,
$$
using $\cos^2x=(1+\cos2x)/2$. Therefore
$$
\boxed{k=\frac2\pi.}
$$
= Solution
{c}
Normalization of the <probability density function> requires
$$
1=k\int_{-\pi/2}^{\pi/2}\cos^2x\,dx=k\frac\pi2,
$$
using $\cos^2x=(1+\cos2x)/2$. Therefore
$$
\boxed{k=\frac2\pi.}
$$