Let X i , i=1,2 be independent exponential randomvariables with rate i . LetZ=mi
ID: 2914097 • Letter: L
Question
Let Xi , i=1,2 be independent exponential randomvariables with rate i . LetZ=min{X1,X2}. Define a random variable N as N=1 , if Z=X1 N=2 , if Z=X2 Computer P{Z>x , N=1}. ================================================== that variable N block me, i have no idea how to solve thisquestion..... thanks for help. Let Xi , i=1,2 be independent exponential randomvariables with rate i . LetZ=min{X1,X2}. Define a random variable N as N=1 , if Z=X1 N=2 , if Z=X2 Computer P{Z>x , N=1}. ================================================== that variable N block me, i have no idea how to solve thisquestion..... thanks for help. Computer P{Z>x , N=1}. ================================================== that variable N block me, i have no idea how to solve thisquestion..... thanks for help.Explanation / Answer
N=1 , if min{X1,X2} =X1 N=2 , if min{X1,X2} =X2 P{Z>x , N=1} =P{min{X1,X2}>x , N=1} =P{X1>x} =1-P{X1<x} =1-{1-exp(-1 x)} since X is independentexponential r.v. =exp(-1 x) P{Z>x , N=1} =P{min{X1,X2}>x , N=1} =P{X1>x} =1-P{X1<x} =1-{1-exp(-1 x)} since X is independentexponential r.v. =exp(-1 x)Related Questions
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