Question:
Let X be uniformly distributed on (0,1). Show that Y=- [tex]\lambda[/tex]^{-1} 1n(1-X) has an exponential distribution with parameter [tex]\lambda[/tex]>0
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You can also use the standard formula for computing the density of a strictly increasing function. If X has density f_X(x) and Y=g(X) is strictly increasing, then Y has density f_Y(y)=f_X(g^-1(y))*dg^-1(y)/dy
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