part19

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

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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
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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 /
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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− + <
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part19 - ECE 863 Analysis of Stochastic Systems Fall 2001...

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