Question

A random process is stationary

• A. If all statistical properties do not change with time
• B. If the future values of any sample function can be predicted from present values only
• C. Future values cannot be predicted
• D. If the future values of any sample function can be predicted from past values only

Hint:

A stationary random process has time-invariant statistical properties such as mean, variance and autocorrelation.

Answer 1

The Correct Option is A

Concept: A random process is said to be stationary when its statistical characteristics remain unchanged with time. Typical statistical properties include: \[ \text{Mean} \] \[ \text{Variance} \] \[ \text{Autocorrelation} \]

Step 1: Define stationarity.
For a stationary process, \[ m_X(t)=\text{constant} \] and \[ R_X(t_1,t_2) = R_X(t_1-t_2) \] Thus statistical behavior is independent of the absolute time origin.

Step 2: Evaluate the options.
Prediction of future values is related to predictability and not stationarity. Stationarity only requires that statistical properties remain unchanged with time.

Step 3: Final Answer.
Therefore, \[ \boxed{\text{All statistical properties do not change with time}} \] Hence, \[ \boxed{\text{Correct Option (A)}} \]