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

Question

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 .

Answer 1

a)
a = 1
b= -1
c = -1

b)
a = -2
b = -1
c = 1

All are correct!