題組內容

3. Let $Y = a \cos(\omega t + \Theta)$ where a, $\omega$ and t are constants, and $\Theta$ is a uniform random variable in the interval $(0, 2\pi)$. The random variable Y results from sampling the amplitude of a sinusoid with random phase $\Theta$. (5% each, total 10%)

(a) Find the expected value of \( Y \).