Thread: Probability and Stochastic Process - Stationary

I have a question.
Show that if a normal process is WSS, then it is also SSS?
WSS(wide sense stationary) and SSS(strict sense stationary)

Originally Posted by ebigood

I have a question.
Show that if a normal process is WSS, then it is also SSS?
WSS(wide sense stationary) and SSS(strict sense stationary)

In case this is a homework problem, I'll only give you hints that you can use to solve it yourself.

A process is WSS if its first and second moments are time invariant. All of the moments of an SSS process are time invariant.

That should be enough for you to figure out the answer to your question.

In wss
E{x(t+c)}=E{x(t)} and E{x(t+c)^2}=E{x(t)^2} now How i can Generalize this to all moments and i proof that is sss. Please Guidance me.

Originally Posted by ebigood

In wss
E{x(t+c)}=E{x(t)} and E{x(t+c)^2}=E{x(t)^2} now How i can Generalize this to all moments and i proof that is sss. Please Guidance me.

If a random variable is normally distributed, then all moments can be expressed as functions of the mean and variance.