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Unformatted text preview: SS1.1.(d)2. Solution to this problem will be posted separately.SS2.(a)P[X<5,Y >2,Z22] =P[X<5]P[Y >2]P[Z22]=P[5< X <5](1P[Y2])(1P[2< Z <2])= [FX(5)FX(5)][1FY(2)][1FZ(2) +FZ(2)](b)P[X >5,Y <,Z= 1] =P[X >5]P[Y <0]P[Z= 1]= [1FX(5)]FY(0)[FZ(1)FZ(1)](c)P[min(X,Y,Z)>2] =P[X >2]P[Y >2]P[Z >2]= [1FX(2)][1FY(2)][1FZ(2)](d)P[max(X,Y,Z)<6] =P[X <6]P[Y <6]P[Z <6]=FX(6)FY(6)FZ(6)SS3.yyyFigure 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+dyyyyydyFigure 2: Event{yYy+dy}shown in black. Mapping to function shown in blue. Equivashown 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.
 Spring '11
 Wang

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