2
$\begingroup$

Let's say I define random variable $\varphi$ is uniformly distributed between $[0,2\pi).$

I then define Random process $y(t)=\sin(2\pi t+\varphi)$

Is this process SSS? For now, let's assume that the definition of SSS is that the PDF is not conditional on $t$

What about

$$z(t)=\sin^2\left(2\pi t+\varphi\right) \text{ ?}$$

  • 0
    What is the meaning of SSS? _Strictly Stationary_ processes require not just that each $Y(t)$ has the same distribution, but also that for each $n > 1$ and time instants $t_1, t_2, \ldots, t_n$, $Y(t_1), Y(t_2), \ldots, Y(t_n)$ have the same _joint_ distribution as $Y(t_1+\tau), Y(t_2+\tau), \ldots, Y(t_n+\tau)$. Where do you verify that this holds? – 2017-02-09

0 Answers 0