Normal Random Variable - Random Signals and Processes Primer with MATLAB - page 256

a

2 =5 2 =8

X1: m=1, σ X2: m=2.6, σ

20

10

5

10

0

0

− 5

− 10 0

− 10

5000 10000 0 5000 10000

n n

X=X1+X2

20

10

0

− 10

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

n

b

X1 X2

0.2 0.2

0.15 0.15

0.1 0.1

0.05 0.05

0 0

− 20 − 10 0 10 20 − 20 − 10 0 10 20

x1 x2

X=X1+X2

0.2

0.15

0.1

0.05

0

− 15 − 10 − 5 0 5 10 15 20

− 20

x

Fig. 4.17 Illustration of the sum of normal random variables. ( a ) Normal variables. ( b ) PDFs