Consider a random process $X(t) = \sqrt{2}\sin(2\pi t + \varphi),$ where the random phase $\varphi$ is uniformly distributed in the interval $[0,2\pi].$ The auto-correlation $E[X(t_{1})X(t_{2})]$ is
- $\cos(2\pi(t_{1} + t_{2}))$
- $\sin(2\pi(t_{1} - t_{2}))$
- $\sin(2\pi(t_{1} + t_{2}))$
- $\cos(2\pi(t_{1} - t_{2}))$