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標題:
P(1 smaller X smaller 2Y)
發問:
given X~N(10,100) Y~N(16,144) X,Y are independent variable find P(1 < X < 2Y) by transform it into Z
最佳解答:
I'm not sure whether the below answer is correct or not. P(1<2Y)=Intersection of P(X>1) and P(X<2Y) ***(Please draw a graph for Illustration) Since X~N(10,100), (X-10)/10~N(0,1)=Z Let W=X-2Y; then W~N(-22,388); and (W+22)/sqrt(388)~N(0,1)=Z P(X>1)=P[ (X-10)/10>(1-10)/10 ] ..........=P(Z>-0.9) ..........=1-P(Z<-0.9)=0.816 P(X<2Y)=P(X-2Y<0) ............=P[ (W+22)/sqrt(388)<22/sqrt(388)] ............=P(Z<1.12) ............=0.869 Since X and Y are independent, P(1<2Y)=Intersection of P(X>1) and P(X<2Y) ................=P(X>1) X P(X<2Y) ................=0.816X0.869=0.709 2007-10-16 19:20:47 補充： P(1<2Y) should read P(1 < X < 2Y)
P(1 smaller X smaller 2Y)
發問:
given X~N(10,100) Y~N(16,144) X,Y are independent variable find P(1 < X < 2Y) by transform it into Z
最佳解答:
I'm not sure whether the below answer is correct or not. P(1<2Y)=Intersection of P(X>1) and P(X<2Y) ***(Please draw a graph for Illustration) Since X~N(10,100), (X-10)/10~N(0,1)=Z Let W=X-2Y; then W~N(-22,388); and (W+22)/sqrt(388)~N(0,1)=Z P(X>1)=P[ (X-10)/10>(1-10)/10 ] ..........=P(Z>-0.9) ..........=1-P(Z<-0.9)=0.816 P(X<2Y)=P(X-2Y<0) ............=P[ (W+22)/sqrt(388)<22/sqrt(388)] ............=P(Z<1.12) ............=0.869 Since X and Y are independent, P(1<2Y)=Intersection of P(X>1) and P(X<2Y) ................=P(X>1) X P(X<2Y) ................=0.816X0.869=0.709 2007-10-16 19:20:47 補充： P(1<2Y) should read P(1 < X < 2Y)
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