are these random processes strict sense stationary?

From: lucy (losemind_at_yahoo.com)
Date: 11/25/04 

Date: Thu, 25 Nov 2004 00:24:06 -0800

Hi all,

Please help in identify whether the following random processes are strict
sense stationry or not...

1) X(t)=cos(2*pi*t+THETA) where THETA is uniform in [0, 2*pi]... what if
THETA is exponentially distributed in [0, +inf]?

2) Y(t)=g(t-THETA) where g(t) is a sawtooth function which is periodical
with period T, the sawtooth function has shape like this: it is 1 at t=0, it
is 0 at t=T, then it jumps(discontinuity) to 1 at t=T, and then it is zero
at t=2T(discontinuity), so on and so forth. THETA is uniform in [0, T].

What if THETA is exponentially distributed in [0, +inf]?

I want to identify which are the keys of deciding the random processes to be
SSS or WSS or not...

The shape of the function, such as cos(t), g(t), etc?

Or the property of the R.V. in that function, such as uniform, exponential
distribution, etc.?

Any thoughts?

Thanks a lot and happy holiday!

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