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In the absence of more details, I assume that the phase $\Theta$ is a random variable and $\Theta$ is uniformly distributed on the interval $[0,2\pi]$, so that its probability density function is $\frac{1}{2\pi}$ on that interval. This is a common choice of model for such problems, and I will show that its guarantees that the stochastic process $x$ is wide-...