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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

  1. $\cos(2\pi(t_{1} + t_{2}))$
  2. $\sin(2\pi(t_{1} - t_{2}))$
  3. $\sin(2\pi(t_{1} + t_{2}))$
  4. $\cos(2\pi(t_{1} - t_{2}))$
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