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The random variable X is exponential with parameter λ=1 . The random variable Y is defined by Y=g(X)=1/(1+X) .

a) The inverse function h , for which h(g(x))=x , is of the form ay^b+c . Find a , b , and c .

b) For y∈(0,1] , the PDF of Y is of the form fY(y)=y^a*e^((b/y)+c) . Find a , b , and c .

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4 answers

  1. a) (y^-1)-1 So a=1,b=-1,c=-1

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  2. b)y^-2*e^(-1/y+1). so a=-2,b=-1,c=1

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  3. h(x) = 1/x - 1 = (1-x)/x
    so, ...

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  4. so yes h(x) = 1/x - 1 = (1-x)/x
    but what do you do then?
    derivative of (1-x)/x = -1/x^2

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