Islamic University of Gaza Probability and Stochastic Processes

Faculty of Engineering EELE 3340

Electrical Engineering Department Fall semester 2011/2012

Problem Set #6 Solution

Problem(1)

For the following Gaussian R.V,

the peak value is 0.4

(a) Find the expected value and standard deviation.

(b) Sketch the ().

2

2

6 9

2

2

1( )

2

x x

Xf x e

2 2

2 2

6 9 ( 3)

2 2

2 2

2

1 1( )

2 2

3

1( 3) 0.4 1

2

x x x

X

X

f x e e

mean

f x

Solution

Problem(2)

Find the value of the following probabilities:

a ( > 1.26) b ( < 0.86) c > 1.37 d 1.25 < < 0.37

(a) ( 1.26) 1 ( 1.26) 1 (1.26) 1 0.89616 0.10384

(b) 0.86) 1 (0.86) 1 0.8051 0.1949

(c) 1.37) 1 1.37) 1 1 (1.37) (1.37) 0.9147

(d) 1.25 0.37) (0.37) ( 1.25) (0.

P Z P Z

P(Z