- #1
Addem
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Homework Statement
(From Probability and Statistical Inference, Hogg and Tanis, Eighth Edition, 5.1-5)
The p.d.f. of X is [itex]f(x) = \theta x^{\theta - 1}[/itex] for [itex]0<x<1[/itex] and [itex]0<\theta<\infty[/itex]. Let [itex]Y = -2\theta \ln X[/itex]. How is [itex]Y[/itex] distributed?
Homework Equations
Um... Fundamental Theorem of Calculus?
The Attempt at a Solution
So I've actually solved this, it's exponential with [itex]\theta = 2[/itex]. My question is about the answer given in the back of the book: It cryptically says [itex]M(t) = (1-2t)^{-1}[/itex] for [itex]t<1/2[/itex] which is, to my eye, a useless calculation of the moment-generating function. WTF? Why is this here? Ideas?
Thank you.