Transforming functions of random variables (exponential->Weibull)

[slaux89]

Homework Statement

Suppose X has an exponential with parameter L and Y=X^(1/a).
Find the density function of Y. This is the Weibull distribution

Homework Equations

The Attempt at a Solution

X~exponential (L) => fx(s)= Le^(-Ls)

Fx(s)=P(X<s) = 1-e^(-Ls)

P(Y<s)=P(X^(1/a)<s)=P(X<s^a)= 1-e^(-L[s^a])= Fy(s)

thus fy(s) = La(s^[a-1])e^(-L[s^a))

However, this doesn't seem to be the Weibull distribution. Did I do something wrong? Or is this just a variation of it?

 

[╔(σ_σ)╝]

Looks fine to me.

 

[slaux89]

Alright, thanks!