1. ## Weibull problem

Hi all, I have this question on weibull but was not taught weibull in class. The text book didnt offer much weibull examples or solutions as well. Hope to have some assistance. thanks.

Random variable Q has density f(q) = (lamda)(alpha)(q with power alpha minus 1) x ((e with power negative (lamda)(q with power alpha)) for q > 0 and 0 otherwise.

Prove that (Q with power alpha) is distributed as an exponential random variable with para lamda.

my lousy solution for now is that:

let (q with power alpha) = 1,

then (lamda)(alpha)(q with power alpha minus 1) x ((e with power negative (lamda)(q with power alpha)) =

(lamda)(alpha)(1 with power minus 1) x ((e with power negative (lamda)(1)) =

(lamda)(alpha)(e with power negative lamda) =

exponential function with (lamda) = Exp(lamda)

very

2. A formal proof would involve getting the pdf of a transformed variable Z=Q^a, i.e f(Z^(1/a))*|dQ/dZ| and go on. You can find that technique in Probability books, under tranformation of r.v's or look for Jacobian at the index

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