soln4 - SS-1.1.(d)2. Solution to this problem will be posted

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Unformatted text preview: SS-1.1.(d)2. Solution to this problem will be posted separately.SS-2.(a)P[|X|<5,Y >2,Z22] =P[|X|<5]P[Y >2]P[Z22]=P[-5< X <5](1-P[Y2])(1-P[-2< Z <2])= [FX(5-)-FX(-5)][1-FY(2)][1-FZ(2-) +FZ(-2)](b)P[X >5,Y <,Z= 1] =P[X >5]P[Y <0]P[Z= 1]= [1-FX(5)]FY(0-)[FZ(1)-FZ(1-)](c)P[min(X,Y,Z)>2] =P[X >2]P[Y >2]P[Z >2]= [1-FX(2)][1-FY(2)][1-FZ(2)](d)P[max(X,Y,Z)<6] =P[X <6]P[Y <6]P[Z <6]=FX(6-)FY(6-)FZ(6-)SS-3.y-yyFigure 1: Event{Yy}shown in black. Mapping to function shown in blue. Equivalent eventshown in orange.From Figure 1,{Yy}={-yXy}, y,,y <FY(y) =P(Yy)=P(-yXy), y,otherwise=FX(y)-FX(-y), y,otherwisefY(y) =ddyFY(y) =fX(y) +fX(-y), y,otherwiseNote that you should be careful in taking the derivative of a function that is defined piecewiseover some range. However, in this case the function is continuous aty= 0, soy= 0is nota special case.b)y+dyy+dyyy-y-y-dyFigure 2: Event{yYy+dy}shown in black. Mapping to function shown in blue. Equiva-shown in black....
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This note was uploaded on 01/29/2012 for the course ECE 101 taught by Professor Wang during the Spring '11 term at Iowa State.

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soln4 - SS-1.1.(d)2. Solution to this problem will be posted

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