part19

# part19 - ECE 863 Analysis of Stochastic Systems Fall 2001...

This preview shows pages 1–4. Sign up to view the full content.

1 ECE 863 – Analysis of Stochastic Systems Fall 2001 Solutions for Homework Set #3 Michigan State University Department of Electrical & Computer Engineering Problem 1 3.51 P Y 3.5d P Y e dx 3d x == = -= -• - z a a 2 α = 1 -3 d 2 e P Y 2.5d P Y 2.5d e 2 dx 3d 2d x = - - z a a =- -- 1 2 ee 2d 3d aa ot S i m i l a r l y , {} αα = =   -d - 1 PY 1 .5d PY - 1 e e 2 P Y 0.5d P Y 1 2 1e d = - -a PY 4 d 2 e 2 dx e 4d x >= = - - z a a a

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Problem 2 3.53 When X is Gaussian f Y = a X + b is also Gaussian where: m' E Y aE X b am b == + = + ss ' bg 2 22 a =f a = s s ' bm ' m =- s s ' Problem 3 3.56 Power P RX 2 Fy PR X y F y/R F y 0 p 2 XX e j e j - " f= + - = +- fy / R 2R y/R / R f f 2R y p xx b g ej e j e j f 1 y e p 2 y2 2 R = - F H I K ps s /
3 Problem 4 3.58 (a) "< £ = + £ = - y 0PY y PX a y F y a x bg "= £ = £ = y 0PY 0 F a x "> £ = - £ = + y y F y a x () x xx Y x fya y 0 fy Fa F a y y 0 −< =− δ = +> (b) If fx 2 e x x = - a a then it can be easily shown that: α −α < = −≥ x X x 1 ex 0 2 Fx 1 1e x 0 2 This leads to: ya Y 1 ey 0 2 Fy 1 y 0 2 α− + <

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 9

part19 - ECE 863 Analysis of Stochastic Systems Fall 2001...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online