Hi everyone.

I have started few days ago studying stochastical processes, and I'm trying to do and exercise that has me stuck.
Is the following:

1\bulletIf X(t) is a mean square differentiable wide-sense stationary stochastical process then the processes X(t) and X' (t) are orthogonal.


2\bulletIf X(t) is a twice mean square differentiable, stationary and Gaussian stochastical process, such that
E[X(t)] = 0, then X(t) is independent of X' (t) but not independent of
X''(t)


My teacher told me to use the formula: \Gamma_{X^{(n)},X^{(m)}}(t,s)=(-1)^m\frac{d^{(n+m)}\Gamma_X(\tau)}{d\tau^{(n+m)}}, where \tau=t-s, but it seems to get me nowhere...


Thanks a lot for any help.