EVOLUTIONARY 
STATIONARY UP TO 1ST ORDER 
ERGODIC UP TO 2ND ORDER 
STATIONARY UP TO 2ND ORDER 
COMPLETELY STATIONARY 
AND ERGODIC 
Fig. 2.1. Stationarity and ergodicity. 
For example, 
R(t) =E [X(t) -X(t+7)] 
| | X(t)X(t + T) Pt, X147)AX1AX 141 
T 
1 
lim) | x(t)x(t + T)dt. 
Be GP Ir (2.5) 
2.1.5 Summary of Gaussian (Normal) Probability Distribution Functions 
For convenience, the Gaussian probability distribution functions for various num- 
bers of variables are summarized here. For a single variable, 
1 1 @aonJF 
p() = (Qno2V2 ex - 5 aie j (2.6) 
Normalized by z = (x—fx)/0,, 
(Ne ee eS 2.7) 
zZ) =—— €?. 3 
Nay eae 
For two variables X and Y 
