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